What separates a vector quantity from a scalar quantity?

A vector has magnitude and direction; a scalar has magnitude only. Velocity is a vector, while speed is a scalar.

When is the point-object model useful in kinematics?

When an object's size and rotation do not matter for the motion being studied. Its position can then represent the whole object.

When may the constant-acceleration kinematic equations be used?

Only over an interval with constant acceleration. They are not general formulas for changing acceleration.

Why must a velocity statement name or imply a reference frame?

Velocity depends on the observer's frame. The same object can be at rest in one frame and moving in another.

Why can horizontal and vertical projectile motion be analyzed separately?

Perpendicular components evolve independently. With negligible air resistance, gravity changes only the vertical component.

Can an object have zero velocity and nonzero acceleration at one instant?

Yes. At the top of a vertical toss, velocity is momentarily zero while gravitational acceleration still points downward.

A runner completes one lap and returns to the start. How do distance and displacement compare?

The distance is one lap, while the displacement is zero. Displacement depends only on the change from initial to final position.

What makes a reference frame convenient for a motion problem?

It makes the relevant positions or velocities simple. A good frame reduces bookkeeping without changing physical predictions.

How are the components of a launch velocity v at angle θ found?

v_x = v cos θ and v_y = v sin θ. The angle is measured from the positive horizontal axis.

What does average velocity measure?

Displacement per elapsed time. In one dimension, v_avg = Δx/Δt; direction comes from the sign of Δx.

Do a vector's magnitude and its component use different SI units?

No. A vector and each of its components use the same unit; for example, velocity and its x-component both use m/s.

A velocity-versus-time graph curves upward and becomes progressively steeper while staying above zero. What does that show?

The object moves in the positive direction and speeds up with increasing positive acceleration. The graph's slope is acceleration; because that slope changes, the acceleration is nonuniform.

What are a projectile's horizontal and vertical accelerations when air resistance is negligible and up is positive?

a_x = 0 and a_y = -g. Horizontal velocity stays constant while vertical velocity changes.

What does average acceleration measure?

Change in velocity per elapsed time. In one dimension, a_avg = Δv/Δt.

What does a negative one-dimensional vector component mean?

It points opposite the chosen positive direction. The minus sign describes direction, not a negative physical size.

For constant acceleration, what does v = v₀ + at retrieve?

Velocity after elapsed time t. Use it when initial velocity, constant acceleration, and time are known or related.

How are a vector's magnitude and direction reconstructed from perpendicular components v_x and v_y?

v = √(v_x² + v_y²). When v_x ≠ 0, use θ = tan⁻¹(v_y/v_x) and the component signs to choose the quadrant. If v_x = 0 and v_y ≠ 0, the vector points along +y or -y; if both components are zero, its direction is undefined.

At an instant when velocity is nonzero, how do velocity and acceleration signs show whether a one-dimensional object is speeding up?

It speeds up when velocity and acceleration have the same sign. Opposite signs mean speed is decreasing at that instant.

What does the slope of a position-versus-time graph represent?

Velocity. A steeper slope means a larger speed, and the slope's sign gives direction.

Two observers use inertial frames, where an object with zero net force has constant velocity. If the observers move at constant velocity relative to each other, do they agree on an object's acceleration?

Yes, in a Galilean inertial-frame model. Subtracting a constant frame velocity changes velocity but not acceleration. This definition distinguishes an inertial frame from an accelerating, noninertial frame.

A projectile lands at its launch height with negligible air resistance. How do its launch and landing speeds compare?

They are equal. The horizontal component is unchanged, and the vertical component returns with equal magnitude and opposite sign.

A car's velocity changes from -2 m/s to +6 m/s in 2 s. What is its average acceleration?

+4 m/s². Δv = 8 m/s, and 8 m/s ÷ 2 s = 4 m/s².

If the positive axis is reversed, what happens to a one-dimensional vector component and its magnitude?

The component changes sign, while the magnitude stays the same. A coordinate choice changes the signed description, not the physical vector.

For constant acceleration, what does Δx = v₀t + ½at² retrieve?

Displacement over time t. It includes both initial-velocity motion and the displacement added by constant acceleration.

For a horizontal launch from height h in uniform gravity with negligible air resistance, what sets the time to reach the ground?

The vertical drop alone. Starting with v_y = 0, the time follows h = ½gt² and does not depend on horizontal speed.

Why can average speed differ from the magnitude of average velocity?

Average speed uses total distance, while average velocity uses displacement. Reversing direction increases distance without necessarily increasing displacement.

What does the slope of a velocity-versus-time graph represent?

Acceleration. The slope's units are (m/s)/s = m/s².

A passenger walks forward at 2 m/s inside a train moving forward at 18 m/s. What is the passenger's ground velocity?

20 m/s forward. Add the passenger's train-relative velocity to the train's ground velocity.

Does projectile mass affect the ideal trajectory when air resistance is negligible?

No. All projectiles have the same gravitational acceleration, so equal initial conditions give equal trajectories.

Can an object have nonzero velocity and zero acceleration?

Yes. Constant-velocity motion has nonzero velocity while the velocity change, and therefore acceleration, is zero.

A cart starts from rest with constant acceleration. Which graph should be linear if x = x₀ + ½at² applies?

Position x versus t². Its slope is ½a when the initial velocity is zero.

What does signed area under a velocity-versus-time graph represent?

Displacement. Area below the time axis contributes negative displacement.

At the highest point of a projectile's path, what are its vertical velocity and vertical acceleration?

v_y = 0, but a_y = -g. The vertical velocity pauses before reversing; gravity does not switch off.

How can a motion sensor test whether a cart moves at constant velocity?

Record position at equal time intervals and graph position versus time. A straight line with nearly constant slope supports constant velocity.

A car passes a parked observer at 12 m/s. What is the parked observer's velocity in the car's frame?

-12 m/s. In the car's frame, the ground and observer move backward at the car's speed.

Which constant-acceleration equation connects speed and displacement without using time?

v² = v₀² + 2aΔx. Use signed one-dimensional quantities and constant acceleration.

How could video data test the independence of projectile components?

Track x and y at equal times. A linear x-versus-t graph and a quadratic vertical trend support constant horizontal velocity and vertical acceleration.

A velocity-versus-time graph stays below zero but slopes upward toward zero. What is happening?

The object moves in the negative direction while slowing down. Velocity is negative and acceleration is positive.

How can average velocity over a very short interval approximate instantaneous velocity?

Shrink the time interval around the instant. The displacement divided by that short interval approaches the local position–time graph slope.

A walker moves 7 m east, then 3 m west. What is the one-dimensional displacement if east is positive?

+4 m. Add signed displacements: +7 m + (-3 m) = +4 m.

What shape is the path of a projectile with a nonzero horizontal velocity component in a uniform gravitational field when air resistance is negligible?

A parabola. Constant horizontal velocity and constant vertical acceleration produce the curve. A purely vertical launch is the special case: its spatial path is a vertical line.

In a motion diagram with dots at equal time intervals and velocity arrows, what do wider dot spacing and longer arrows show?

Greater speed. Wider spacing means more distance is covered during each equal time interval, while longer velocity arrows represent a larger velocity magnitude. Each arrow points in the direction of motion.

What does signed area under an acceleration-versus-time graph represent?

Change in velocity. Add that signed area to the initial velocity to find the final velocity.

How is one-dimensional relative velocity calculated for two objects A and B?

v_A relative to B = v_A - v_B. Both velocities must be measured in the same frame before subtracting.

When its speed is nonzero, what direction does a projectile's instantaneous velocity point?

Tangent to its path. Its horizontal and vertical velocity components combine to set that direction.

What does choosing a system boundary decide in a mechanics problem?

It decides which objects belong to the system and which forces count as external. Internal interactions occur between objects inside the boundary.

What belongs on a free-body diagram for one chosen object?

Only forces exerted on that object by other objects. Do not draw velocity, acceleration, or forces the chosen object exerts elsewhere.

What assumptions define the ideal-string model used in introductory algebra-based physics?

The string is massless, inextensible, and flexible. It pulls along its length, doesn't stretch, and can redirect around an ideal pulley.

What does translational equilibrium require?

Zero net force. The object may be at rest or move with constant velocity.

In an inertial frame, how does Newton's second law connect force and motion?

ΣF = ma. The net external force on the chosen object or system causes its acceleration; mass sets how strongly the velocity responds.

How do mass and weight differ?

Mass measures inertia in kilograms; weight is gravitational force in newtons. Near a surface, F_g = mg.

AP Physics 1 Flashcards: Complete 8-Unit Course Review

A 400-card AP Physics 1 review of concepts, formulas, graphs, experiments, and reasoning across all eight course units.

Umbhali Open Study Contributor

Mayelana naleli qoqo

This 400-card deck reviews all eight AP Physics 1 course units: Kinematics; Force and Translational Dynamics; Work, Energy, and Power; Linear Momentum; Torque and Rotational Dynamics; Energy and Momentum of Rotating Systems; Oscillations; and Fluids.

What you'll retrieve

Choose the governing principle for a situation or claim, then explain the prediction in plain language.
Recall what a quantity or equation means, when it applies, how it scales, and which SI unit it uses.
Read slopes, signed areas, extrema, signs, and shapes across motion, force, energy, momentum, rotation, oscillation, and fluid graphs.
Plan a small experiment by naming useful variables, measurements, controls, linearized graphs, slope meanings, and uncertainty checks.
Solve one focused original algebra-based setup with units and a short reason.
Use selected reverse and contrast prompts to recognize conditions and separate common confusion pairs.

The deck does not mechanically reverse every fact. Bare formula-to-symbol lists, long multipart calculations, and imitation exam questions are excluded.

The sequence follows Units 1–8 so motion, forces, energy, and momentum become prerequisites for rotation, orbits, oscillations, and fluids. Definitions appear before dependent uses, while related formula, graph, condition, calculation, and contrast prompts are separated where practical to reduce short-range cueing.

Course scope was checked against the official AP Physics 1 course page. Every prompt, answer, numerical setup, explanation, ordering choice, and metadata field was independently written from common physics knowledge. The CC0 label applies to that original expression and organization to the extent applicable rights exist; it does not claim ownership of physics facts or third-party material.

This is an independently authored, unofficial educational deck. It is not affiliated with, sponsored by, or endorsed by the College Board. AP® is a trademark registered by the College Board, which is not affiliated with, and does not endorse, this product. No AP exam questions, answer keys, scoring guidelines, curriculum text, logos, or trade dress were copied.

Amakhadi akuleli qoqo

Ikhadi 1
Umbuzo
What separates a vector quantity from a scalar quantity?
Impendulo
A vector has magnitude and direction; a scalar has magnitude only. Velocity is a vector, while speed is a scalar.
Ikhadi 2
Umbuzo
When is the point-object model useful in kinematics?
Impendulo
When an object's size and rotation do not matter for the motion being studied. Its position can then represent the whole object.
Ikhadi 3
Umbuzo
When may the constant-acceleration kinematic equations be used?
Impendulo
Only over an interval with constant acceleration. They are not general formulas for changing acceleration.
Ikhadi 4
Umbuzo
Why must a velocity statement name or imply a reference frame?
Impendulo
Velocity depends on the observer's frame. The same object can be at rest in one frame and moving in another.
Ikhadi 5
Umbuzo
Why can horizontal and vertical projectile motion be analyzed separately?
Impendulo
Perpendicular components evolve independently. With negligible air resistance, gravity changes only the vertical component.
Ikhadi 6
Umbuzo
Can an object have zero velocity and nonzero acceleration at one instant?
Impendulo
Yes. At the top of a vertical toss, velocity is momentarily zero while gravitational acceleration still points downward.
Ikhadi 7
Umbuzo
A runner completes one lap and returns to the start. How do distance and displacement compare?
Impendulo
The distance is one lap, while the displacement is zero. Displacement depends only on the change from initial to final position.
Ikhadi 8
Umbuzo
What makes a reference frame convenient for a motion problem?
Impendulo
It makes the relevant positions or velocities simple. A good frame reduces bookkeeping without changing physical predictions.
Ikhadi 9
Umbuzo
How are the components of a launch velocity v at angle θ found?
Impendulo
v_x = v cos θ and v_y = v sin θ. The angle is measured from the positive horizontal axis.
Ikhadi 10
Umbuzo
What does average velocity measure?
Impendulo
Displacement per elapsed time. In one dimension, v_avg = Δx/Δt; direction comes from the sign of Δx.
Ikhadi 11
Umbuzo
Do a vector's magnitude and its component use different SI units?
Impendulo
No. A vector and each of its components use the same unit; for example, velocity and its x-component both use m/s.
Ikhadi 12
Umbuzo
A velocity-versus-time graph curves upward and becomes progressively steeper while staying above zero. What does that show?
Impendulo
The object moves in the positive direction and speeds up with increasing positive acceleration. The graph's slope is acceleration; because that slope changes, the acceleration is nonuniform.
Ikhadi 13
Umbuzo
What are a projectile's horizontal and vertical accelerations when air resistance is negligible and up is positive?
Impendulo
a_x = 0 and a_y = -g. Horizontal velocity stays constant while vertical velocity changes.
Ikhadi 14
Umbuzo
What does average acceleration measure?
Impendulo
Change in velocity per elapsed time. In one dimension, a_avg = Δv/Δt.
Ikhadi 15
Umbuzo
What does a negative one-dimensional vector component mean?
Impendulo
It points opposite the chosen positive direction. The minus sign describes direction, not a negative physical size.
Ikhadi 16
Umbuzo
For constant acceleration, what does v = v₀ + at retrieve?
Impendulo
Velocity after elapsed time t. Use it when initial velocity, constant acceleration, and time are known or related.
Ikhadi 17
Umbuzo
How are a vector's magnitude and direction reconstructed from perpendicular components v_x and v_y?
Impendulo
v = √(v_x² + v_y²). When v_x ≠ 0, use θ = tan⁻¹(v_y/v_x) and the component signs to choose the quadrant. If v_x = 0 and v_y ≠ 0, the vector points along +y or -y; if both components are zero, its direction is undefined.
Ikhadi 18
Umbuzo
At an instant when velocity is nonzero, how do velocity and acceleration signs show whether a one-dimensional object is speeding up?
Impendulo
It speeds up when velocity and acceleration have the same sign. Opposite signs mean speed is decreasing at that instant.
Ikhadi 19
Umbuzo
What does the slope of a position-versus-time graph represent?
Impendulo
Velocity. A steeper slope means a larger speed, and the slope's sign gives direction.
Ikhadi 20
Umbuzo
Two observers use inertial frames, where an object with zero net force has constant velocity. If the observers move at constant velocity relative to each other, do they agree on an object's acceleration?
Impendulo
Yes, in a Galilean inertial-frame model. Subtracting a constant frame velocity changes velocity but not acceleration. This definition distinguishes an inertial frame from an accelerating, noninertial frame.
Ikhadi 21
Umbuzo
A projectile lands at its launch height with negligible air resistance. How do its launch and landing speeds compare?
Impendulo
They are equal. The horizontal component is unchanged, and the vertical component returns with equal magnitude and opposite sign.
Ikhadi 22
Umbuzo
A car's velocity changes from -2 m/s to +6 m/s in 2 s. What is its average acceleration?
Impendulo
+4 m/s². Δv = 8 m/s, and 8 m/s ÷ 2 s = 4 m/s².
Ikhadi 23
Umbuzo
If the positive axis is reversed, what happens to a one-dimensional vector component and its magnitude?
Impendulo
The component changes sign, while the magnitude stays the same. A coordinate choice changes the signed description, not the physical vector.
Ikhadi 24
Umbuzo
For constant acceleration, what does Δx = v₀t + ½at² retrieve?
Impendulo
Displacement over time t. It includes both initial-velocity motion and the displacement added by constant acceleration.
Ikhadi 25
Umbuzo
For a horizontal launch from height h in uniform gravity with negligible air resistance, what sets the time to reach the ground?
Impendulo
The vertical drop alone. Starting with v_y = 0, the time follows h = ½gt² and does not depend on horizontal speed.
Ikhadi 26
Umbuzo
Why can average speed differ from the magnitude of average velocity?
Impendulo
Average speed uses total distance, while average velocity uses displacement. Reversing direction increases distance without necessarily increasing displacement.
Ikhadi 27
Umbuzo
What does the slope of a velocity-versus-time graph represent?
Impendulo
Acceleration. The slope's units are (m/s)/s = m/s².
Ikhadi 28
Umbuzo
A passenger walks forward at 2 m/s inside a train moving forward at 18 m/s. What is the passenger's ground velocity?
Impendulo
20 m/s forward. Add the passenger's train-relative velocity to the train's ground velocity.
Ikhadi 29
Umbuzo
Does projectile mass affect the ideal trajectory when air resistance is negligible?
Impendulo
No. All projectiles have the same gravitational acceleration, so equal initial conditions give equal trajectories.
Ikhadi 30
Umbuzo
Can an object have nonzero velocity and zero acceleration?
Impendulo
Yes. Constant-velocity motion has nonzero velocity while the velocity change, and therefore acceleration, is zero.
Ikhadi 31
Umbuzo
A cart starts from rest with constant acceleration. Which graph should be linear if x = x₀ + ½at² applies?
Impendulo
Position x versus t². Its slope is ½a when the initial velocity is zero.
Ikhadi 32
Umbuzo
What does signed area under a velocity-versus-time graph represent?
Impendulo
Displacement. Area below the time axis contributes negative displacement.
Ikhadi 33
Umbuzo
At the highest point of a projectile's path, what are its vertical velocity and vertical acceleration?
Impendulo
v_y = 0, but a_y = -g. The vertical velocity pauses before reversing; gravity does not switch off.
Ikhadi 34
Umbuzo
How can a motion sensor test whether a cart moves at constant velocity?
Impendulo
Record position at equal time intervals and graph position versus time. A straight line with nearly constant slope supports constant velocity.
Ikhadi 35
Umbuzo
A car passes a parked observer at 12 m/s. What is the parked observer's velocity in the car's frame?
Impendulo
-12 m/s. In the car's frame, the ground and observer move backward at the car's speed.
Ikhadi 36
Umbuzo
Which constant-acceleration equation connects speed and displacement without using time?
Impendulo
v² = v₀² + 2aΔx. Use signed one-dimensional quantities and constant acceleration.
Ikhadi 37
Umbuzo
How could video data test the independence of projectile components?
Impendulo
Track x and y at equal times. A linear x-versus-t graph and a quadratic vertical trend support constant horizontal velocity and vertical acceleration.
Ikhadi 38
Umbuzo
A velocity-versus-time graph stays below zero but slopes upward toward zero. What is happening?
Impendulo
The object moves in the negative direction while slowing down. Velocity is negative and acceleration is positive.
Ikhadi 39
Umbuzo
How can average velocity over a very short interval approximate instantaneous velocity?
Impendulo
Shrink the time interval around the instant. The displacement divided by that short interval approaches the local position–time graph slope.
Ikhadi 40
Umbuzo
A walker moves 7 m east, then 3 m west. What is the one-dimensional displacement if east is positive?
Impendulo
+4 m. Add signed displacements: +7 m + (-3 m) = +4 m.
Ikhadi 41
Umbuzo
What shape is the path of a projectile with a nonzero horizontal velocity component in a uniform gravitational field when air resistance is negligible?
Impendulo
A parabola. Constant horizontal velocity and constant vertical acceleration produce the curve. A purely vertical launch is the special case: its spatial path is a vertical line.
Ikhadi 42
Umbuzo
In a motion diagram with dots at equal time intervals and velocity arrows, what do wider dot spacing and longer arrows show?
Impendulo
Greater speed. Wider spacing means more distance is covered during each equal time interval, while longer velocity arrows represent a larger velocity magnitude. Each arrow points in the direction of motion.
Ikhadi 43
Umbuzo
What does signed area under an acceleration-versus-time graph represent?
Impendulo
Change in velocity. Add that signed area to the initial velocity to find the final velocity.
Ikhadi 44
Umbuzo
How is one-dimensional relative velocity calculated for two objects A and B?
Impendulo
v_A relative to B = v_A - v_B. Both velocities must be measured in the same frame before subtracting.
Ikhadi 45
Umbuzo
When its speed is nonzero, what direction does a projectile's instantaneous velocity point?
Impendulo
Tangent to its path. Its horizontal and vertical velocity components combine to set that direction.
Ikhadi 46
Umbuzo
What does choosing a system boundary decide in a mechanics problem?
Impendulo
It decides which objects belong to the system and which forces count as external. Internal interactions occur between objects inside the boundary.
Ikhadi 47
Umbuzo
What belongs on a free-body diagram for one chosen object?
Impendulo
Only forces exerted on that object by other objects. Do not draw velocity, acceleration, or forces the chosen object exerts elsewhere.
Ikhadi 48
Umbuzo
What assumptions define the ideal-string model used in introductory algebra-based physics?
Impendulo
The string is massless, inextensible, and flexible. It pulls along its length, doesn't stretch, and can redirect around an ideal pulley.
Ikhadi 49
Umbuzo
What does translational equilibrium require?
Impendulo
Zero net force. The object may be at rest or move with constant velocity.
Ikhadi 50
Umbuzo
In an inertial frame, how does Newton's second law connect force and motion?
Impendulo
ΣF = ma. The net external force on the chosen object or system causes its acceleration; mass sets how strongly the velocity responds.
Ikhadi 51
Umbuzo
How do mass and weight differ?
Impendulo
Mass measures inertia in kilograms; weight is gravitational force in newtons. Near a surface, F_g = mg.
Ikhadi 52
Umbuzo
How does static friction choose its magnitude before slipping begins?
Impendulo
It matches the needed tangential contact force up to a maximum. In general, f_s ≤ μ_sN.
Ikhadi 53
Umbuzo
For an ideal spring in its linear range, what is the spring force when its end is displaced by a signed amount x from the relaxed or natural length?
Impendulo
F_s = -kx. The sign shows that the spring force opposes the signed extension or compression and points toward the relaxed or natural length.
Ikhadi 54
Umbuzo
What direction does centripetal acceleration point in circular motion?
Impendulo
Toward the circle's center. It changes the velocity's direction even when speed is constant.
Ikhadi 55
Umbuzo
What is the gravitational force magnitude between two point masses?
Impendulo
F_g = Gm₁m₂/r². Here r is the center-to-center separation.
Ikhadi 56
Umbuzo
Why isn't the normal force always equal to an object's weight?
Impendulo
It adjusts to the contact and acceleration conditions. Other vertical forces or vertical acceleration can change its magnitude.
Ikhadi 57
Umbuzo
What determines a friction coefficient in the simple model?
Impendulo
The pair of contacting materials and their surface condition. It isn't a universal property of either material alone.
Ikhadi 58
Umbuzo
What is the centripetal-acceleration magnitude for speed v and radius r?
Impendulo
a_c = v²/r. It is a kinematic requirement, not a separate force.
Ikhadi 59
Umbuzo
An elevator accelerates upward. How does the scale reading compare with a rider's weight?
Impendulo
It is greater than the weight. Upward net force requires N - mg > 0.
Ikhadi 60
Umbuzo
What does a spring constant k measure, and what is its SI unit?
Impendulo
It measures stiffness in N/m. A larger k means more force is needed for the same displacement in the linear range.
Ikhadi 61
Umbuzo
Three equal point masses are at (0,0), (3 m,0), and (0,3 m). Where is their center of mass?
Impendulo
At (1 m,1 m). Average the x-coordinates and y-coordinates separately for equal masses.
Ikhadi 62
Umbuzo
What provides centripetal force?
Impendulo
The inward component of real forces such as tension, gravity, friction, or a normal force. 'Centripetal force' names their net inward result.
Ikhadi 63
Umbuzo
How is near-surface gravitational field strength related to weight?
Impendulo
F_g = mg. The local field strength g has units N/kg, equivalent to m/s².
Ikhadi 64
Umbuzo
How is weight resolved on an incline of angle θ measured from horizontal?
Impendulo
mg sin θ points down the slope and mg cos θ points into the slope. These are components of one gravitational force.
Ikhadi 65
Umbuzo
What does Newton's third law say about an interaction between objects A and B?
Impendulo
The force of A on B and the force of B on A have equal magnitude and opposite direction. They act on different objects.
Ikhadi 66
Umbuzo
What does signed tangential acceleration describe during circular motion?
Impendulo
It describes how quickly speed changes and which way the tangential acceleration points along the chosen tangent. Its magnitude is the absolute value of the instantaneous rate of change of speed. If it points with the velocity, speed increases; if it points against the velocity, speed decreases. Its sign follows the chosen tangent.
Ikhadi 67
Umbuzo
What happens to gravitational force if the separation between two point masses doubles?
Impendulo
It becomes one-fourth as large. The force follows an inverse-square dependence on distance.
Ikhadi 68
Umbuzo
How can an adjustable incline estimate a block's coefficient of static friction when no other applied force acts?
Impendulo
Raise the incline slowly until the block just begins to slide. At that threshold, the simple block model gives μ_s = tan θ.
Ikhadi 69
Umbuzo
In an inertial frame, what determines the acceleration of a fixed-mass system's center of mass?
Impendulo
The net external force divided by the system's total mass. Internal force pairs cannot change the center-of-mass motion of the whole system.
Ikhadi 70
Umbuzo
Which tension components act for a conical pendulum?
Impendulo
The vertical component balances weight, and the horizontal component supplies centripetal force. The bob moves in a horizontal circle.
Ikhadi 71
Umbuzo
What does apparent weight measure for an object supported by one surface?
Impendulo
The normal-force magnitude exerted by that support. It can differ from gravitational force when the object accelerates.
Ikhadi 72
Umbuzo
How are several forces combined to find net force?
Impendulo
Add them as vectors, component by component. Opposing components subtract according to the chosen signs.
Ikhadi 73
Umbuzo
Why is tension uniform along one continuous ideal string?
Impendulo
Every massless segment must have zero net force in the ideal model. Without frictional contact or a massive pulley changing it, the tension magnitude stays the same throughout the string.
Ikhadi 74
Umbuzo
A 0.5 kg object moves at 4 m/s in a circle of radius 2 m. What inward net force is required?
Impendulo
4 N. F_in = mv²/r = 0.5 × 16 / 2.
Ikhadi 75
Umbuzo
What local equivalence links a uniform gravitational field with a uniformly accelerating reference frame?
Impendulo
A uniform gravitational field and a uniformly accelerating reference frame can produce the same local mechanical effects. Local observations alone may not distinguish them.
Ikhadi 76
Umbuzo
For the same net force, what happens to acceleration if mass doubles?
Impendulo
Acceleration is halved. From a = ΣF/m, acceleration is inversely proportional to mass.
Ikhadi 77
Umbuzo
How do static and kinetic friction coefficients usually compare for the same pair of surfaces?
Impendulo
Typically μ_s > μ_k. Starting sliding usually requires a larger friction threshold than maintaining it.
Ikhadi 78
Umbuzo
How are radial and tangential acceleration combined when circular speed changes?
Impendulo
Add the perpendicular components as vectors. The total magnitude is √(a_c² + a_t²).
Ikhadi 79
Umbuzo
A spherically symmetric planet has twice Earth's mass and the same radius. How does its surface g compare with Earth's?
Impendulo
It is twice as large. Surface field strength follows g = GM/R².
Ikhadi 80
Umbuzo
Does a force have to point in the direction of motion?
Impendulo
No. A force points in the direction of the interaction; it may speed up, slow down, or turn the object.
Ikhadi 81
Umbuzo
Where is the center of mass of a uniform object with a symmetric mass distribution?
Impendulo
At its geometric center of symmetry. Symmetry lets opposite mass elements balance without a detailed sum.
Ikhadi 82
Umbuzo
How are speed, period, and frequency related in uniform circular motion?
Impendulo
v = 2πr/T = 2πrf, with T = 1/f. One cycle covers one circumference.
Ikhadi 83
Umbuzo
Why is an object apparently weightless in free fall?
Impendulo
Its support force is zero while it and its surroundings accelerate together under gravity. Gravity still acts.
Ikhadi 84
Umbuzo
Can forces balance along one axis while an object accelerates along another?
Impendulo
Yes. Zero net force in one component gives zero acceleration only in that direction; another component can remain unbalanced.
Ikhadi 85
Umbuzo
Why don't Newton's third-law forces cancel on one object's free-body diagram?
Impendulo
Only one force in the pair acts on that object. The partner force belongs on the other object's diagram.
Ikhadi 86
Umbuzo
On a frictionless banked curve, which force components create vertical balance and inward acceleration?
Impendulo
The normal force's vertical component balances weight, while its horizontal component supplies the inward net force.
Ikhadi 87
Umbuzo
What motion results when the net force on an object is zero in an inertial frame?
Impendulo
Constant velocity. Rest is the special case with constant velocity equal to zero.
Ikhadi 88
Umbuzo
A 3 kg cart has a net horizontal force of 12 N. What is its acceleration?
Impendulo
4 m/s². Use a = ΣF/m = 12/3.
Ikhadi 89
Umbuzo
What does the observed equivalence of inertial and gravitational mass imply for free fall?
Impendulo
Free-fall acceleration is independent of the falling object's mass. Inertial and gravitational mass are proportional and conventionally assigned equal numerical values.
Ikhadi 90
Umbuzo
Does friction in the simple dry-friction model depend on apparent contact area?
Impendulo
No. For a fixed normal force and the same contacting materials, the model treats friction magnitude as independent of apparent contact area.
Ikhadi 91
Umbuzo
When should Hooke's-law predictions be treated cautiously?
Impendulo
When deformation leaves the spring's linear elastic range. Force may no longer be proportional to displacement.
Ikhadi 92
Umbuzo
What bank angle θ supports speed v on an ideal frictionless curve of radius r?
Impendulo
tan θ = v²/(rg). The result assumes no vertical acceleration and no friction.
Ikhadi 93
Umbuzo
Why do internal forces cancel when finding the net force on a complete system?
Impendulo
They occur in equal-and-opposite pairs between system parts. Each pair sums to zero in the system's force total.
Ikhadi 94
Umbuzo
An elevator moves downward at constant speed. How does the scale reading compare with weight?
Impendulo
It equals the weight. Constant velocity means zero acceleration and N - mg = 0.
Ikhadi 95
Umbuzo
What assumptions let an ideal pulley redirect a string without changing its tension magnitude?
Impendulo
The pulley is massless and frictionless, and the string is ideal. It changes the tension's direction while the magnitude stays the same on both sides.
Ikhadi 96
Umbuzo
What does inertia describe?
Impendulo
An object's resistance to changes in velocity. Mass measures translational inertia.
Ikhadi 97
Umbuzo
For the same fixed-mass object or system across all measurements, what does the slope of a net-force-versus-acceleration graph represent?
Impendulo
Its mass. Written as ΣF = ma, the graph has slope m when the object or system and its mass stay fixed.
Ikhadi 98
Umbuzo
Does zero net force mean no forces act?
Impendulo
No. Several forces can act and cancel vectorially.
Ikhadi 99
Umbuzo
What is the common model for kinetic-friction magnitude?
Impendulo
f_k = μ_kN. It applies while the surfaces slide under the model's assumptions.
Ikhadi 100
Umbuzo
How could hanging masses measure the spring constant of one ideal spring?
Impendulo
At static equilibrium, record the spring's extension for several known weights and graph mg versus extension. Keep the same spring in its linear range; the slope is k.
Ikhadi 101
Umbuzo
For the same object at the same circular radius, how does required inward net force change if speed doubles?
Impendulo
It becomes four times as large. F_in = mv²/r depends on speed squared.
Ikhadi 102
Umbuzo
Where is the center of mass of two point masses on an x-axis?
Impendulo
At x_cm = (m₁x₁ + m₂x₂)/(m₁ + m₂). It lies closer to the larger mass.
Ikhadi 103
Umbuzo
Why must net force, rather than one selected force, be used in ΣF = ma?
Impendulo
All external forces contribute to acceleration. Ignoring a force changes the vector sum and the prediction.
Ikhadi 104
Umbuzo
Why can tension vary along a hanging chain with nonnegligible mass?
Impendulo
Higher sections must support and accelerate more chain below them. Newton's third law still applies locally to each interaction; it does not make tension uniform everywhere.
Ikhadi 105
Umbuzo
What makes a reference frame inertial?
Impendulo
An object with zero net force has constant velocity in that frame. A frame accelerating relative to an inertial frame is noninertial.
Ikhadi 106
Umbuzo
How could carts test the proportionality between acceleration and net force?
Impendulo
Keep total mass constant, vary the applied net force, and graph acceleration versus force. A line through the origin supports a ∝ ΣF.
Ikhadi 107
Umbuzo
How does Kepler's third-law scaling compare two satellites in circular orbits at center-to-center radii r when their masses are negligible relative to the same fixed central mass?
Impendulo
T² ∝ r³. The circular orbit with the larger center-to-center radius has the longer period.
Ikhadi 108
Umbuzo
Which direction does kinetic friction act?
Impendulo
Opposite the relative sliding of the contacting surfaces. It is not automatically opposite the object's velocity in every frame.
Ikhadi 109
Umbuzo
What does the slope of a spring-force-versus-displacement graph give?
Impendulo
-k when signed force is graphed against signed displacement. The slope magnitude is the spring constant.
Ikhadi 110
Umbuzo
What is the minimum speed at the top of an ideal vertical loop of radius r when gravity alone supplies the inward force?
Impendulo
v_min = √(gr). At the threshold, the support force or tension is zero.
Ikhadi 111
Umbuzo
What is translational kinetic energy?
Impendulo
Energy associated with an object's translational motion. For a point-like object, K = ½mv².
Ikhadi 112
Umbuzo
How is work by a constant force calculated when its point of application undergoes a straight displacement?
Impendulo
W = Fd cos θ. Here d is the displacement of the force's point of application, and θ is the angle between the force and that displacement.
Ikhadi 113
Umbuzo
What does power measure?
Impendulo
The rate of energy transfer or conversion. P_avg = ΔE_transferred/Δt; when work is the relevant transfer, P_avg = W/Δt.
Ikhadi 114
Umbuzo
What does conservation of energy say for an isolated system?
Impendulo
The system's total energy stays constant. Energy may change form or move among system parts, but it is not created or destroyed.
Ikhadi 115
Umbuzo
Can translational kinetic energy be negative?
Impendulo
No. Mass is positive and speed is squared, so translational kinetic energy is zero or positive.
Ikhadi 116
Umbuzo
What does negative work by a force mean?
Impendulo
The force makes a negative contribution to the system's kinetic-energy change. Its component opposes the displacement of its point of application; potential energy may rise while total mechanical energy stays constant.
Ikhadi 117
Umbuzo
What is the near-surface change in gravitational potential energy?
Impendulo
ΔU_g = mgΔy. It applies when g can be treated as constant.
Ikhadi 118
Umbuzo
When is a chosen system's mechanical energy K + U conserved?
Impendulo
When no net energy crosses the system boundary and no internal process converts energy in either direction between mechanical and nonmechanical forms. If either condition fails, K + U can change even though total energy still balances for the system plus surroundings.
Ikhadi 119
Umbuzo
What is the SI unit of power?
Impendulo
The watt, W. One watt equals one joule per second.
Ikhadi 120
Umbuzo
For an object modeled as a particle, what connects net work by all forces to its change in translational kinetic energy?
Impendulo
The work–energy theorem: W_net = ΔK. Under the particle model, positive net work raises translational kinetic energy and negative net work lowers it. A rotating rigid system requires total kinetic energy and work at the forces' points of application.
Ikhadi 121
Umbuzo
A ball falls from rest through height h near a planet's surface. For the ball–planet system, g is constant and air resistance is negligible. What speed does energy conservation predict?
Impendulo
v = √(2gh). The system's mgh decrease in gravitational potential energy becomes ½mv².
Ikhadi 122
Umbuzo
Does choosing a different zero level for potential energy change physical predictions?
Impendulo
No. Only potential-energy differences enter measurable energy changes.
Ikhadi 123
Umbuzo
Can an engine do the same work with different average power?
Impendulo
Yes. Doing the same work in less time requires greater average power.
Ikhadi 124
Umbuzo
When does a constant nonzero force do zero work over an interval?
Impendulo
When its point of application has zero displacement or its displacement is perpendicular to the force. Then W = Fd cos θ is zero.
Ikhadi 125
Umbuzo
A particle-modeled block slides down a fixed frictionless track. Does the path shape affect its final speed at a given lower height?
Impendulo
No. With only gravity doing work, the potential-energy change depends on height, not path.
Ikhadi 126
Umbuzo
How does translational kinetic energy change if speed doubles at constant mass?
Impendulo
It becomes four times as large. Kinetic energy depends on v².
Ikhadi 127
Umbuzo
What is the elastic potential energy of an ideal spring displaced by a signed amount x from its relaxed or natural length, with U_s = 0 there?
Impendulo
U_s = ½kx². Choosing zero energy at the relaxed length gives the same stored energy for equal-magnitude extension or compression.
Ikhadi 128
Umbuzo
What does signed area under a force-component-versus-position graph represent when position tracks that force's point of application?
Impendulo
Work done by that force along the measured coordinate. Area below the position axis counts as negative work under the graph's sign convention.
Ikhadi 129
Umbuzo
A chosen system starts with 20 J of mechanical energy and converts 6 J of it into thermal energy, with no energy crossing the boundary. How much mechanical energy remains?
Impendulo
14 J. The 6 J thermal-energy increase matches the mechanical-energy decrease.
Ikhadi 130
Umbuzo
What shape does a translational-kinetic-energy-versus-speed graph have for fixed mass?
Impendulo
The right-hand half of an upward-opening parabola through the origin. Speed is nonnegative, and K is proportional to v², not v.
Ikhadi 131
Umbuzo
A machine transfers 600 J in 3 s. What is its average power?
Impendulo
200 W. Divide energy transferred by elapsed time.
Ikhadi 132
Umbuzo
Why does the normal force do no work on a nonrotating block sliding across a fixed horizontal floor?
Impendulo
The force is perpendicular to the horizontal displacement of its points of application. Their dot product is zero in this pure-translation model.
Ikhadi 133
Umbuzo
A coaster modeled as a particle moves on a fixed frictionless track. Where is its speed greatest?
Impendulo
At the lowest accessible position. Gravitational potential energy is smallest there, so kinetic energy is largest.
Ikhadi 134
Umbuzo
Two objects have equal mass and velocities of equal magnitude but opposite direction. How do their translational kinetic energies compare?
Impendulo
They are equal. Kinetic energy uses speed and has no direction.
Ikhadi 135
Umbuzo
What makes work by a conservative force path independent?
Impendulo
It depends only on the initial and final configurations. Any two paths between the same endpoints give the same conservative-force work.
Ikhadi 136
Umbuzo
A 10 N force acts while its point of application moves 3 m in the force direction. How much work does the force do?
Impendulo
30 J. Here θ = 0, so W = Fd = 10×3.
Ikhadi 137
Umbuzo
How is total potential energy built for a system with several interacting pairs?
Impendulo
Add the potential energy assigned to each relevant pair. Count each interaction pair once and use one consistent reference choice.
Ikhadi 138
Umbuzo
How should external work appear in an energy equation?
Impendulo
As energy transferred across the system boundary. A useful form is ΔE_system = W_external + other transfers.
Ikhadi 139
Umbuzo
How does a spring launch problem combine energy forms?
Impendulo
Initial elastic energy becomes kinetic energy and possibly gravitational or thermal energy. Write only the forms present in the chosen initial and final states.
Ikhadi 140
Umbuzo
For a constant force parallel to the velocity of its point of application, how is instantaneous mechanical power calculated?
Impendulo
P = Fv. More generally, P = F·v_point, so only the force component along that point's velocity contributes.
Ikhadi 141
Umbuzo
How does translational kinetic energy change if mass triples at constant speed?
Impendulo
It triples. Kinetic energy is directly proportional to mass.
Ikhadi 142
Umbuzo
How much net work does a conservative force do around a path that returns to the initial configuration?
Impendulo
Zero. The initial and final potential energies are the same.
Ikhadi 143
Umbuzo
Where is stable equilibrium on a potential-energy-versus-position graph?
Impendulo
At a local minimum. Small displacements produce forces that point back toward the minimum.
Ikhadi 144
Umbuzo
Which displacement belongs in the work done by a force on a rigid object?
Impendulo
The displacement of that force's point of application. Using the center-of-mass displacement can be wrong when the object also rotates.
Ikhadi 145
Umbuzo
What happens to mechanical energy when kinetic friction acts inside the chosen system?
Impendulo
Some mechanical energy becomes thermal energy. The broader system's total energy still balances.
Ikhadi 146
Umbuzo
A nonrotating particle falls from rest through vertical drop h under constant g. If its gravitational-potential decrease becomes only translational kinetic energy, with no other energy changes, what graph linearizes final speed?
Impendulo
Graph v² versus drop height h. Under those conditions, v² = 2gh, so the slope should be 2g.
Ikhadi 147
Umbuzo
If two students start and finish a stair climb at the same speeds, how could data compare their average mechanical output power against gravity?
Impendulo
Measure each student's mass, vertical rise, and climb time, then calculate mgh/t. Equal initial and final speeds make ΔK = 0; if ΔK is negligible, the result is an approximation. This is mechanical output power against gravity, not metabolic input power.
Ikhadi 148
Umbuzo
How can force-sensor data measure work when force changes as its point of application moves?
Impendulo
Graph the force component along the motion against the point-of-application position and find the signed area. A rectangle formula isn't enough for a varying force.
Ikhadi 149
Umbuzo
Why is potential energy assigned to a system rather than one isolated object?
Impendulo
It belongs to an interaction between system parts. Gravitational potential energy, for example, belongs to the object–Earth system.
Ikhadi 150
Umbuzo
How can work by a nonconservative force depend on path?
Impendulo
Different routes can have different force histories or path lengths. Kinetic-friction work, for example, can change with distance traveled.
Ikhadi 151
Umbuzo
A 2 kg cart moves at 3 m/s. What is its translational kinetic energy?
Impendulo
9 J. K = ½(2)(3²) = 9 J.
Ikhadi 152
Umbuzo
A block slides distance d across a stationary surface while constant kinetic friction f_k opposes its displacement. What work does friction do on the block?
Impendulo
W_f = -f_k d. The negative sign follows from friction pointing opposite the block's displacement in this stated setup.
Ikhadi 153
Umbuzo
A 2 kg object rises 5 m where g = 10 m/s². What is ΔU_g?
Impendulo
+100 J. ΔU_g = mgΔy = 2 × 10 × 5.
Ikhadi 154
Umbuzo
Why are energy bar charts useful?
Impendulo
They make initial energy, final energy, and transfers explicit. A correct chart respects the chosen system and reference levels.
Ikhadi 155
Umbuzo
A motor lifts the same load through the same height twice as fast. Both lifts begin and end at the same speeds and have equal or negligible dissipative losses. How do the motor's mechanical output work and average power compare?
Impendulo
The mechanical output work is unchanged, while average power doubles. The two lifts have the same ΔU_g, the same ΔK, and the same losses, so the same output energy is delivered in half the time.
Ikhadi 156
Umbuzo
A nonrotating 1 kg block starts from rest and receives 18 J of net work. What speed does it reach?
Impendulo
6 m/s. For this pure-translation model, ΔK = 18 J = ½(1)v².
Ikhadi 157
Umbuzo
Why is gravitational potential energy lower when two attracting point masses—or nonoverlapping spherical bodies—are closer in the inverse-square model?
Impendulo
Energy must be supplied to separate them. With zero chosen at infinite center-to-center separation, U_g = -GMm/r.
Ikhadi 158
Umbuzo
What does a steep potential-energy graph imply about force magnitude in one dimension?
Impendulo
A large force magnitude. Force points toward decreasing potential energy and corresponds to the negative slope of U(x).
Ikhadi 159
Umbuzo
An ideal spring with k = 80 N/m is compressed 0.50 m from its relaxed length. With U_s = 0 at that length, what elastic energy is stored?
Impendulo
10 J. U_s = ½(80)(0.50²).
Ikhadi 160
Umbuzo
A constant 50 N force acts while its point of application moves at 4 m/s in the force direction. What mechanical power is delivered?
Impendulo
200 W. P = Fv_point = 50 × 4.
Ikhadi 161
Umbuzo
If potential energy decreases by 30 J and no energy crosses the system boundary, what happens to the other energy forms?
Impendulo
They increase by a total of 30 J. Often kinetic energy rises, but thermal or other forms may share the increase.
Ikhadi 162
Umbuzo
Does an object's translational kinetic energy depend on the reference frame?
Impendulo
Yes. Different inertial observers can measure different speeds and therefore different K = ½mv² for the same object.
Ikhadi 163
Umbuzo
Why can work depend on the system boundary?
Impendulo
Changing the system can reclassify energy transfer. For example, friction may be external work on one system but internal thermal-energy conversion in a larger system.
Ikhadi 164
Umbuzo
A force-component-versus-position graph for the force's point of application forms a triangle of base 4 m and height 6 N above the axis. What work does it show?
Impendulo
12 J. The signed area is ½×4×6.
Ikhadi 165
Umbuzo
A motor transfers 50 J into a chosen system while another device transfers 12 J out. What is the net system-energy change?
Impendulo
+38 J. Add the signed transfers across the boundary: 50 J - 12 J.
Ikhadi 166
Umbuzo
What is the clearest first step in an energy-conservation problem?
Impendulo
Choose the system and the initial and final states. That choice determines which energies and transfers belong in the equation.
Ikhadi 167
Umbuzo
Why can energy methods solve some problems without finding time?
Impendulo
Energy connects states through position, speed, and transfers. Time is absent unless power or a time-dependent process matters.
Ikhadi 168
Umbuzo
Why can a force's instantaneous mechanical power be zero while the force is nonzero?
Impendulo
Its point of application may be instantaneously at rest, or the force may be perpendicular to that point's velocity. In either case F·v_point = 0.
Ikhadi 169
Umbuzo
What is the SI unit of kinetic energy?
Impendulo
The joule, J. One joule equals 1 kg·m²/s².
Ikhadi 170
Umbuzo
How is work by a conservative force related to potential-energy change?
Impendulo
W_conservative = -ΔU. When the conservative force does positive work, potential energy falls.
Ikhadi 171
Umbuzo
Where is unstable equilibrium on a potential-energy-versus-position graph?
Impendulo
At a local maximum. A small displacement produces a force that pushes the system farther away.
Ikhadi 172
Umbuzo
For a particle moving in a circle at constant speed, does the inward net force change its translational kinetic energy?
Impendulo
No. The inward net force is perpendicular to the particle's instantaneous velocity, so its net work is zero and it changes the velocity's direction rather than its magnitude.
Ikhadi 173
Umbuzo
Why should thermal energy not be written as a force?
Impendulo
Thermal energy is an energy store, not an interaction force. Friction is the interaction that converts or transfers energy.
Ikhadi 174
Umbuzo
How could a ramp experiment test mechanical-energy conservation for a cart–Earth system when the cart is modeled as a particle?
Impendulo
Measure speed and height at several points, calculate K + U_g with one consistent zero level, and compare within uncertainty. Systematic drift suggests unmodeled energy transfer or conversion.
Ikhadi 175
Umbuzo
According to the plotted power's definition and sign convention, what does signed area under a power-versus-time graph represent?
Impendulo
Energy transferred or converted over the interval. Interpret positive and negative areas using the graph's stated sign convention and what its power represents.
Ikhadi 176
Umbuzo
What is linear momentum?
Impendulo
p = mv. Momentum is a vector in the direction of velocity and uses SI units kg·m/s.
Ikhadi 177
Umbuzo
How is a multi-object system's total momentum found?
Impendulo
Add every object's momentum as a vector. In one dimension, add signed values.
Ikhadi 178
Umbuzo
For a chosen object or system, what is external impulse?
Impendulo
The change in its momentum: J_external = Δp. For constant net external force, J_external = F_net,external Δt.
Ikhadi 179
Umbuzo
What experimental uncertainty matters strongly when comparing collision kinetic energies?
Impendulo
Velocity uncertainty. Because K depends on v², small speed errors can produce larger relative energy errors.
Ikhadi 180
Umbuzo
Why can two objects bounce apart yet still collide inelastically?
Impendulo
Bouncing does not guarantee kinetic-energy conservation. Some kinetic energy becomes internal or thermal energy through deformation, and some may be carried by sound.
Ikhadi 181
Umbuzo
A 3 kg cart moves right at 4 m/s. What is its momentum if right is positive?
Impendulo
+12 kg·m/s. p = mv = 3 × 4.
Ikhadi 182
Umbuzo
Why can momentum be negative while kinetic energy cannot?
Impendulo
Momentum carries direction through velocity's sign. Kinetic energy depends on speed squared.
Ikhadi 183
Umbuzo
When is a system's total linear momentum conserved?
Impendulo
When the net external impulse is zero or negligible during the interval. Internal impulses cancel in the system total.
Ikhadi 184
Umbuzo
Two equal masses collide elastically in one dimension; one is initially at rest. What commonly happens?
Impendulo
They exchange velocities. The incoming mass stops and the other leaves with its speed under the ideal conditions.
Ikhadi 185
Umbuzo
Can total kinetic energy increase in an explosion?
Impendulo
Yes. Stored internal energy can become kinetic energy. Total momentum is conserved for a defined system with zero or negligible net external impulse, while total energy remains conserved for the system plus surroundings.
Ikhadi 186
Umbuzo
How is total momentum related to center-of-mass velocity?
Impendulo
p_total = Mv_cm. M is the system's total mass.
Ikhadi 187
Umbuzo
How does a nonzero external impulse affect system momentum?
Impendulo
It changes total momentum by that impulse. J_external = Δp_system.
Ikhadi 188
Umbuzo
Two carts start at rest and push apart with negligible external horizontal impulse. How do their final momenta compare?
Impendulo
They are equal in magnitude and opposite in direction. The system began with zero total momentum.
Ikhadi 189
Umbuzo
What are equivalent SI units for impulse?
Impendulo
N·s and kg·m/s. Both represent a change in momentum.
Ikhadi 190
Umbuzo
What defines an elastic collision?
Impendulo
Both total momentum and total kinetic energy are conserved for the chosen isolated system. Individual objects may exchange both quantities.
Ikhadi 191
Umbuzo
How can a force sensor and motion detector test the impulse–momentum theorem for one cart?
Impendulo
Account for every external force component along the measured axis, compare the net-force–time area with m(v_f - v_i), and include uncertainty. Agreement supports J_external = Δp.
Ikhadi 192
Umbuzo
A person jumps right from a stationary boat. Neglecting external horizontal impulse, which way does the boat move?
Impendulo
Left. The person and boat acquire opposite momenta so total momentum remains zero.
Ikhadi 193
Umbuzo
Why must momentum signs be kept through an impulse calculation?
Impendulo
Impulse changes a vector quantity. Reversal can make Δp larger than either momentum magnitude alone.
Ikhadi 194
Umbuzo
What defines a perfectly inelastic collision?
Impendulo
The objects stick together after impact. Momentum is conserved in an isolated system, but kinetic energy decreases as much as the constraints allow.
Ikhadi 195
Umbuzo
Why can momentum be conserved during a collision even when large forces act?
Impendulo
For a defined system with zero or negligible net external impulse, the large collision forces are internal. Their equal-and-opposite impulses cancel within that system.
Ikhadi 196
Umbuzo
Two objects have equal speed. Which has the larger momentum magnitude?
Impendulo
The object with larger mass. At equal speed, momentum is proportional to mass.
Ikhadi 197
Umbuzo
How is momentum conservation written for a two-dimensional isolated interaction?
Impendulo
Conserve components separately: Σp_x,i = Σp_x,f and Σp_y,i = Σp_y,f. Both component equations must hold for the same interaction.
Ikhadi 198
Umbuzo
For a chosen object or system, how is average net external force related to impulse?
Impendulo
F_avg,external = Δp/Δt. For the same momentum change, a longer interaction time gives a smaller average force.
Ikhadi 199
Umbuzo
Which conservation law alone can determine the shared final velocity of a sticking collision?
Impendulo
Linear momentum conservation, if external impulse is negligible. Kinetic energy is not conserved in the sticking process.
Ikhadi 200
Umbuzo
Two equal momentum vectors point along +x and +y. What direction does their total momentum point?
Impendulo
At 45° between the positive axes. Equal perpendicular components produce that resultant direction.
amakhadi angu-400
AP Physics 1 Flashcards: Complete 8-Unit Course Review
Funda leli qoqo mahhala
I-Nibomo iyavuleka ukuze uqale ukufunda.
Ikhadi 201
Umbuzo
If external impulse during a collision is small but not zero, what should experimental data show?
Impendulo
Final total momentum should be close to, but not exactly equal to, initial total momentum. The difference estimates external impulse.
Ikhadi 202
Umbuzo
A force–time pulse has the same area but twice the peak force and half the duration. How does its impulse change?
Impendulo
It does not change. Impulse depends on total signed area, not peak force alone.
Ikhadi 203
Umbuzo
A 1 kg cart at 4 m/s sticks to an identical stationary cart. If external impulse is negligible, how does final kinetic energy compare with the initial 8 J?
Impendulo
It is 4 J, half the initial value. The 4 J decrease in translational kinetic energy becomes internal or thermal energy through deformation, and some energy may be carried by sound.
Ikhadi 204
Umbuzo
How can a nearly frictionless cart track improve a momentum-conservation test?
Impendulo
It reduces external horizontal impulse during the collision. That makes the two-cart system closer to isolated.
Ikhadi 205
Umbuzo
How does an object's momentum change if its speed doubles at constant mass?
Impendulo
Its momentum magnitude doubles. Momentum depends linearly on speed.
Ikhadi 206
Umbuzo
For a chosen object or system, what does signed area under its net-external-force-versus-time graph represent?
Impendulo
External impulse, which equals the change in that object's or system's momentum. Area below the time axis contributes negative impulse under the graph's sign convention.
Ikhadi 207
Umbuzo
A firework at rest explodes into two pieces with negligible external impulse. If one piece has twice the mass, how do the piece speeds compare?
Impendulo
The heavier piece moves at half the speed of the lighter piece. Their momentum magnitudes must match.
Ikhadi 208
Umbuzo
Why is sticking evidence of an inelastic collision?
Impendulo
The objects share one final velocity, while some translational kinetic energy becomes internal or thermal energy through deformation. Translational kinetic energy is not conserved.
Ikhadi 209
Umbuzo
Can a moving two-object system have zero total momentum?
Impendulo
Yes. Equal and opposite momenta cancel even though each object is moving.
Ikhadi 210
Umbuzo
A constant 6 N net external force acts on a chosen object for 0.5 s. What impulse does it deliver?
Impendulo
3 N·s in the force direction. Multiply the net external force by the interaction time.
Ikhadi 211
Umbuzo
What does a momentum-versus-velocity graph's slope represent for one object?
Impendulo
Its mass. The relationship p = mv is linear through the origin.
Ikhadi 212
Umbuzo
A 2 kg cart at +3 m/s sticks to a 1 kg cart at rest. If external horizontal impulse is negligible, what is their final velocity?
Impendulo
+2 m/s. Momentum conservation gives (2×3 + 1×0)/(2+1).
Ikhadi 213
Umbuzo
An isolated two-dimensional interaction has known initial total momentum p_total,i and known first outgoing momentum p₁,f. How is the second outgoing momentum found?
Impendulo
Subtract component by component: p₂,f = p_total,i - p₁,f. Thus p₂x,f = p_total,x,i - p₁x,f, with the same subtraction for y.
Ikhadi 214
Umbuzo
A 2 kg ball changes velocity from +3 m/s to -1 m/s. What impulse acts on it?
Impendulo
-8 N·s. Δp = m(v_f - v_i) = 2(-1 - 3).
Ikhadi 215
Umbuzo
What remains conserved in an isolated inelastic collision?
Impendulo
Total momentum. Some kinetic energy becomes internal or thermal energy through deformation, and some may be carried by sound.
Ikhadi 216
Umbuzo
Why does choosing both colliding objects as the system simplify momentum analysis?
Impendulo
Their contact forces become internal. Only external impulse can change the system total.
Ikhadi 217
Umbuzo
For a chosen object or system, what does the slope of its momentum-versus-time graph represent?
Impendulo
Net external force. A steeper slope means a larger force in the slope's signed direction.
Ikhadi 218
Umbuzo
Why do airbags reduce injury force during a stop?
Impendulo
They increase the stopping time for roughly the same momentum change. That lowers the average force.
Ikhadi 219
Umbuzo
A 1 kg cart at 4 m/s sticks to an identical stationary cart. If external impulse is negligible, what final speed do they share?
Impendulo
2 m/s. Momentum 4 kg·m/s is shared by 2 kg.
Ikhadi 220
Umbuzo
For a defined collision system with zero or negligible net external impulse, how can before-and-after velocity measurements classify the collision?
Impendulo
First verify total momentum within uncertainty, then compare total kinetic energy. Unchanged kinetic energy supports elastic behavior; any change beyond uncertainty means the collision isn't elastic, with a decrease indicating an ordinary inelastic collision.
Ikhadi 221
Umbuzo
What is angular displacement?
Impendulo
The signed angle through which a rigid body rotates. In calculations, radians make the linear–angular relationships direct.
Ikhadi 222
Umbuzo
For a rigid body rotating about a chosen fixed axis, what does angular velocity measure?
Impendulo
Signed angular displacement per time about that axis. Average angular velocity is ω_avg = Δθ/Δt under one sign convention.
Ikhadi 223
Umbuzo
For a rigid body rotating about a chosen fixed axis, what does angular acceleration measure?
Impendulo
Change in signed angular velocity per time about that axis. Average angular acceleration is α_avg = Δω/Δt.
Ikhadi 224
Umbuzo
What does rotational inertia measure?
Impendulo
Resistance to angular acceleration about a specified axis. It depends on mass and how that mass is distributed relative to the axis.
Ikhadi 225
Umbuzo
What is the lever arm in a torque calculation?
Impendulo
The perpendicular distance from the axis to the force's line of action. It is not always the full distance to the contact point.
Ikhadi 226
Umbuzo
For a planar rigid object in an inertial frame, what two conditions give simultaneous translational and rotational equilibrium?
Impendulo
ΣF_external = 0 and Στ_external = 0 about a fixed axis. Static equilibrium also requires the object to be at rest.
Ikhadi 227
Umbuzo
Two points lie on the same rotating rigid disk. Which rotational quantities are the same?
Impendulo
They share angular displacement, angular velocity, and angular acceleration. Their linear speeds and accelerations can differ with radius.
Ikhadi 228
Umbuzo
How is rotational inertia found for a collection of point masses?
Impendulo
I_total = Σmᵢrᵢ². Each rᵢ is that mass's perpendicular distance from the chosen axis.
Ikhadi 229
Umbuzo
What determines the magnitude of torque from one force about a chosen axis?
Impendulo
τ = rF sin θ = r_perp F. The radius vector r runs from the axis to the force's point of application, θ is the angle between r and the force, and r_perp is the lever arm.
Ikhadi 230
Umbuzo
What is Newton's second law for a rigid system rotating about an axis fixed in an inertial frame?
Impendulo
Στ_external = Iα when rotational inertia I about that axis is constant. Net external torque and angular acceleration use the same signed-axis convention.
Ikhadi 231
Umbuzo
For a point on a rigid body rotating about a fixed axis, how is signed arc displacement related to signed angular displacement in radians?
Impendulo
Δs = rΔθ. Here r is the point's perpendicular distance from the fixed axis, and both displacements use matching sign conventions along the circular path.
Ikhadi 232
Umbuzo
In a planar rigid-body model, can an object with zero net external force and zero net external torque about its center of mass be moving?
Impendulo
Yes. Its center of mass may translate at constant velocity while it rotates at constant angular velocity; the stated zero net force and center-of-mass torque don't require rest.
Ikhadi 233
Umbuzo
At an instant when ω ≠ 0, what do the signs of angular velocity and angular acceleration show about rotational speed?
Impendulo
Matching signs mean the rotation speeds up; opposite signs mean it slows down. The sign convention chooses which rotation direction is positive.
Ikhadi 234
Umbuzo
How are clockwise and counterclockwise torques combined?
Impendulo
Choose one direction as positive and add signed torques. Net torque is the algebraic sum about the same axis.
Ikhadi 235
Umbuzo
For the same rigid system with constant rotational inertia about the same axis fixed in an inertial frame, what happens if net-external-torque magnitude doubles?
Impendulo
Angular-acceleration magnitude doubles. Under those conditions, |α| is directly proportional to |Στ_external|.
Ikhadi 236
Umbuzo
Why must an axis be named when stating rotational inertia?
Impendulo
The same object has different rotational inertia about different axes. Mass distribution relative to the chosen axis changes.
Ikhadi 237
Umbuzo
For one rigid body rotating about a fixed axis, what does the slope of its angular-position-versus-time graph represent?
Impendulo
Signed angular velocity about that axis. A constant slope means constant angular velocity under the graph's sign convention.
Ikhadi 238
Umbuzo
Why is torque's unit N·m not called a joule?
Impendulo
Torque and energy are different physical quantities despite matching unit dimensions. Torque describes rotational effectiveness of a force.
Ikhadi 239
Umbuzo
A rigid wheel has constant I = 2 kg·m² about an axis fixed in an inertial frame and net external torque 8 N·m about that axis. What is its angular-acceleration magnitude?
Impendulo
4 rad/s². |α| = |Στ_external|/I = 8/2.
Ikhadi 240
Umbuzo
Where can the weight of a rigid object be treated as acting in a uniform gravitational field?
Impendulo
At the object's center of mass. That single force gives the same net gravitational force and torque.
Ikhadi 241
Umbuzo
For a point on a rigid body rotating about a fixed axis, how is tangential-speed magnitude related to angular velocity?
Impendulo
v_t = r|ω|. Here r is the perpendicular distance from the fixed axis. Points farther from the axis move faster even though the rigid body has one angular velocity.
Ikhadi 242
Umbuzo
For constant angular acceleration about one fixed axis, what does ω = ω₀ + αt retrieve?
Impendulo
Angular velocity after elapsed time t. Use signed angular quantities about that axis over an interval with constant α.
Ikhadi 243
Umbuzo
A free-body diagram for a rigid bar must support a torque calculation about a marked axis. What must it show besides each force's direction and magnitude?
Impendulo
Each force's point of application or line of action relative to the axis. That geometry sets the lever arm and torque sign; omitting it can preserve the net-force picture while losing the net torque.
Ikhadi 244
Umbuzo
For the same rigid system about the same axis fixed in an inertial frame, what does the slope of a net-external-torque-versus-angular-acceleration graph represent?
Impendulo
Its constant rotational inertia I about that axis. The graph follows Στ_external = Iα.
Ikhadi 245
Umbuzo
A thin hoop and solid disk have the same mass and radius and rotate about their central symmetry axes. With I_hoop = MR² and I_disk = ½MR², which has larger I?
Impendulo
The hoop. More of its mass lies far from the axis.
Ikhadi 246
Umbuzo
Why can a rigid object have zero net external force but nonzero net external torque?
Impendulo
External forces can cancel as vectors while acting along different lines. The resulting couple can still change the object's rotation.
Ikhadi 247
Umbuzo
Which constant-angular-acceleration equation connects angular velocity and angular displacement about one fixed axis without time?
Impendulo
ω² = ω₀² + 2αΔθ. Use signed quantities about that axis over an interval with constant α.
Ikhadi 248
Umbuzo
A 10 N perpendicular force acts 0.40 m from a pivot. What torque magnitude does it produce?
Impendulo
4 N·m. τ = rF for a perpendicular force.
Ikhadi 249
Umbuzo
For a rigid body rotating about a fixed axis, how is the signed tangential-acceleration component related to angular acceleration?
Impendulo
For a positive tangent consistent with the angular sign convention, a_t = rα. Its alignment or opposition with velocity determines whether speed increases or decreases.
Ikhadi 250
Umbuzo
Why can two equal-mass rigid wheels have different angular-acceleration magnitudes under equal net-external-torque magnitudes about comparable axes fixed in an inertial frame?
Impendulo
Their rotational inertias about those axes can differ because their mass distributions differ. Mass alone doesn't set rotational response.
Ikhadi 251
Umbuzo
For one rigid body rotating about a fixed axis, what does signed area under its angular-velocity-versus-time graph represent?
Impendulo
Signed angular displacement about that axis. Area below the time axis contributes negative angular displacement under the graph's sign convention.
Ikhadi 252
Umbuzo
A rigid object rests on a support that is slowly tilted in uniform gravity. If gravity and support contact are its only external interactions, sufficient static friction prevents slipping, and the motion is quasistatic, what marks the onset of tipping?
Impendulo
The object's center-of-mass vertical line reaches the edge of its support region. Beyond that point, gravity produces an unbalanced tipping torque.
Ikhadi 253
Umbuzo
A point is twice as far from a rigid wheel's fixed axis as another point. How do their tangential speeds compare?
Impendulo
The farther point moves twice as fast. v_t is proportional to radius for their common angular-speed magnitude |ω|.
Ikhadi 254
Umbuzo
Does moving the chosen pivot change an individual force's torque?
Impendulo
Yes. Torque depends on the axis, though a correctly solved physical prediction stays consistent.
Ikhadi 255
Umbuzo
How does the parallel-axis theorem relate rotational inertia to a parallel axis a distance d from the center of mass?
Impendulo
I = I_cm + Md². Shifting the axis away from the center of mass increases rotational inertia.
Ikhadi 256
Umbuzo
How could an experiment determine a rigid wheel's constant rotational inertia about an axis fixed in an inertial frame?
Impendulo
Apply several known signed net external torques about that axis, measure signed angular acceleration, and graph torque versus α. The slope is I.
Ikhadi 257
Umbuzo
For a point at perpendicular distance r > 0 from a rigid body's fixed rotation axis, what is the radial-acceleration magnitude?
Impendulo
a_r = v_t²/r = rω². The acceleration points toward the axis. At r = 0, use a_r = rω² = 0; the quotient form isn't defined there.
Ikhadi 258
Umbuzo
How could a meterstick experiment test torque balance?
Impendulo
Hang known forces at measured lever arms and compare signed r_perp F values at equilibrium. Repeat with different pivot choices.
Ikhadi 259
Umbuzo
For uniform rotation at frequency f, what is the angular-speed magnitude?
Impendulo
|ω| = 2πf. One revolution is 2π rad, and uniform rotation has the same angular-speed magnitude throughout the cycle.
Ikhadi 260
Umbuzo
Why is choosing the pivot at an unknown support force often useful?
Impendulo
That force then has zero lever arm and drops out of the torque equation. The physical equilibrium does not depend on the calculation shortcut.
Ikhadi 261
Umbuzo
Among parallel axes through or near a rigid object, which gives the minimum rotational inertia?
Impendulo
The parallel axis through the center of mass. Any offset adds the positive term Md².
Ikhadi 262
Umbuzo
Compare rigid systems with constant rotational inertia about comparable axes fixed in an inertial frame. If net external torque is the same but I triples, what happens to angular acceleration?
Impendulo
It becomes one-third as large. For each stated system, α = Στ_external/I.
Ikhadi 263
Umbuzo
A rigid wheel of radius 0.50 m has angular-speed magnitude 6 rad/s about its fixed axis. What is the rim speed?
Impendulo
3 m/s. v_t = r|ω| = 0.50 × 6.
Ikhadi 264
Umbuzo
A 30 N child sits 2 m left of a seesaw pivot. If the seesaw's own weight acts through the pivot, where should a 20 N child sit on the right for balance?
Impendulo
3 m from the pivot. Balance torque magnitudes: 30×2 = 20×r.
Ikhadi 265
Umbuzo
For constant angular acceleration about one fixed axis, what does Δθ = ω₀t + ½αt² retrieve?
Impendulo
Angular displacement over elapsed time t. Use signed angular quantities about that axis; the equation combines the initial angular-velocity contribution with the change caused by constant α.
Ikhadi 266
Umbuzo
A 20 N force acts at 30° to a radius vector of magnitude 0.60 m from a chosen axis. What torque magnitude results?
Impendulo
6 N·m. |τ| = rF sin θ = 0.60 × 20 × sin 30°.
Ikhadi 267
Umbuzo
How does moving mass farther from a rotation axis affect rotational inertia?
Impendulo
It increases rotational inertia strongly. For a point mass, I = mr².
Ikhadi 268
Umbuzo
How can angular-acceleration data compare two rigid objects' constant rotational inertias about comparable axes fixed in an inertial frame?
Impendulo
Apply the same measured net-external-torque magnitude about each axis and compare |α|. The object with smaller angular-acceleration magnitude has larger I.
Ikhadi 269
Umbuzo
Why must angular displacement be in radians for Δs = rΔθ?
Impendulo
Radians define angle as arc length divided by radius. Degree measure would require a conversion factor.
Ikhadi 270
Umbuzo
When does a nonzero force produce zero torque about an axis?
Impendulo
When its line of action passes through the axis. The lever arm is then zero.
Ikhadi 271
Umbuzo
What is angular momentum for a rigid object rotating about an axis fixed in an inertial frame?
Impendulo
L = Iω about that axis. Use one signed-axis convention consistently for L and ω.
Ikhadi 272
Umbuzo
What magnitude relation holds for a planar, constant-radius rigid object whose center of mass lies on its rolling axis when it rolls without slipping on a stationary surface?
Impendulo
v_cm = R|ω|. Here R is the constant rolling radius; the contact point is instantaneously at rest relative to the surface.
Ikhadi 273
Umbuzo
For a rigid system rotating about an axis fixed in an inertial frame, how is work by a constant torque about that axis related to angular displacement?
Impendulo
W = τΔθ when torque and angular displacement use the same signed axis. The angle must be in radians.
Ikhadi 274
Umbuzo
For point masses—or nonoverlapping spherical bodies—M and m separated center to center by r, what is gravitational potential energy with zero at infinity?
Impendulo
U_g = -GMm/r. The negative sign reflects U_g = 0 at infinity and attraction. In an isolated gravity-only inverse-square system, total mechanical energy determines binding: E < 0 is bound, while E ≥ 0 is unbound.
Ikhadi 275
Umbuzo
When is a chosen system's angular momentum about an axis fixed in an inertial frame conserved?
Impendulo
When net external torque on the system about that axis is zero or negligible over the interval. Internal torques cannot change the system total.
Ikhadi 276
Umbuzo
What does kinetic friction do to mechanical energy while a wheel slips on a stationary surface?
Impendulo
It converts mechanical energy into internal or thermal energy while the surfaces slide. Use qualitative energy accounting here; no no-slip relation connects the magnitudes v_cm and R|ω| during the slip.
Ikhadi 277
Umbuzo
What is the angular-momentum magnitude of a translating point object about a chosen fixed point in an inertial frame?
Impendulo
L = mvr sin θ = r_perp mv. Here r points from the chosen point to the object, v is its speed, and θ is the angle between them. The SI unit is kg·m²/s.
Ikhadi 278
Umbuzo
For a satellite of negligible mass relative to a fixed central body, how do speed and energy change along one gravity-only elliptical orbit?
Impendulo
Speed and kinetic energy are greatest near the central body, while gravitational potential energy is greatest farther away. Total mechanical energy stays constant.
Ikhadi 279
Umbuzo
What is a rigid body's rotational kinetic energy about a fixed axis?
Impendulo
K_rot = ½Iω². It depends on rotational inertia about that axis and angular speed.
Ikhadi 280
Umbuzo
Two planar rigid objects with constant rolling radii and centers of mass on their rolling axes are released from rest on the same fixed incline. Each rolls without slipping under gravity and its contact forces, with no other applied force or torque and negligible dissipation. Which accelerates faster: the one with smaller or larger I_cm/(MR²)?
Impendulo
The one with smaller I_cm/(MR²). Here I_cm is rotational inertia about the center of mass, M is total mass, and R is that object's constant rolling radius. Under the stated model, a_cm = g sin θ/(1 + I_cm/(MR²)).
Ikhadi 281
Umbuzo
How could a rotating-platform experiment test angular-momentum conservation about the platform's axis, treated as fixed in the lab's inertial frame?
Impendulo
Choose the platform, rider, and moved masses as one system. In both the initial and final arrangements, wait until the rider and moved masses are stationary relative to the platform and the whole system co-rotates with one common signed angular velocity; then measure I_i, ω_i, I_f, and ω_f and compare I_iω_i with I_fω_f. Keep net external torque about the axis negligible, reduce bearing friction, and include uncertainty.
Ikhadi 282
Umbuzo
For a satellite of mass m negligible beside a fixed central mass M, how are K, U_g, and total mechanical energy E related in a gravity-only circular orbit at center-to-center radius r?
Impendulo
K = -U_g/2 and E = U_g/2 = -K. Since U_g = -GMm/r, this gives K = GMm/(2r) and E = -GMm/(2r).
Ikhadi 283
Umbuzo
For a rigid system rotating about an axis fixed in an inertial frame, how is instantaneous mechanical power delivered by a torque about that axis related to angular velocity?
Impendulo
P = τω for signed torque and angular velocity about the same axis. It is the rotational counterpart of P = F·v_point.
Ikhadi 284
Umbuzo
In a planar common-axis rigid-body model, what kinetic-energy expression applies to a body rolling without slipping, with I_cm and ω taken about the same axis through its center of mass?
Impendulo
K = ½Mv_cm² + ½I_cmω². In this model, the rigid body's motion combines center-of-mass translation with rotation about one axis through the center of mass. I_cm and ω must refer to that same axis.
Ikhadi 285
Umbuzo
Does angular-momentum conservation require rotational kinetic-energy conservation?
Impendulo
No. Internal work can change rotational kinetic energy while angular momentum stays constant.
Ikhadi 286
Umbuzo
Why do astronauts feel weightless in orbit even though gravity acts on them?
Impendulo
They and their spacecraft are in continuous free fall together. Apparent weight is small because support forces are small.
Ikhadi 287
Umbuzo
Two wheels spin at the same angular speed. Which has more rotational kinetic energy?
Impendulo
The wheel with larger rotational inertia. At common ω, K_rot is proportional to I.
Ikhadi 288
Umbuzo
For a chosen system, what does the slope of its angular-momentum-versus-time graph about an axis fixed in an inertial frame represent?
Impendulo
Net external torque on the system about that axis. A constant slope means constant signed net external torque there.
Ikhadi 289
Umbuzo
A motor supplies 12 N·m of torque about a shaft axis fixed in the lab's inertial frame while the shaft turns in the torque direction at 10 rad/s. What mechanical power does it deliver?
Impendulo
120 W. Using signed quantities about the shaft axis, P = τω = 12×10.
Ikhadi 290
Umbuzo
While a rigid wheel is slipping on a stationary surface, how are the magnitudes v_cm and R|ω| related?
Impendulo
No no-slip equality applies. Their values evolve separately until friction may bring the contact point to rest relative to the surface.
Ikhadi 291
Umbuzo
A launched object has negligible mass relative to a fixed central mass M and starts at center-to-center radius r. What minimum speed lets it escape under gravity alone without further propulsion or drag?
Impendulo
v_escape = √(2GM/r). At that threshold, total mechanical energy is zero with the object reaching infinity at zero speed.
Ikhadi 292
Umbuzo
In a planar common-axis rigid-body model, what kinetic-energy forms can a rigid body have when it translates and rotates about an axis through its center of mass?
Impendulo
Both translational and rotational kinetic energy. The total is K = ½Mv_cm² + ½I_cmω², where I_cm and ω refer to the same axis through the center of mass.
Ikhadi 293
Umbuzo
For a chosen object or system, what is angular impulse about an axis fixed in an inertial frame?
Impendulo
The change in that object or system's angular momentum about the axis. For constant net external torque, ΔL = τ_net,external Δt. Use the same axis and sign convention throughout. Angular impulse has units N·m·s, equivalent to kg·m²/s.
Ikhadi 294
Umbuzo
Two equal-mass planar rigid objects have constant rolling radii and centers of mass on their rolling axes. They start from rest at the same height and roll without slipping to the same lower endpoint with negligible dissipation. Why can their final speeds differ?
Impendulo
Their rotational inertias divide the same decrease in gravitational potential energy differently between translation and rotation. A larger I_cm/(MR²) leaves less energy for translational speed, where I_cm is rotational inertia about the center of mass and R is rolling radius.
Ikhadi 295
Umbuzo
For a satellite of negligible mass relative to a fixed central body, how does angular momentum behave along one gravity-only elliptical orbit?
Impendulo
It stays constant because gravity exerts zero torque about the central body. The satellite moves faster when closer and slower when farther away.
Ikhadi 296
Umbuzo
How does rotational kinetic energy change if angular speed doubles at fixed I?
Impendulo
It becomes four times as large. Rotational kinetic energy depends on ω².
Ikhadi 297
Umbuzo
Why should external torque be evaluated about the same axis used for angular momentum?
Impendulo
Both quantities depend on the chosen axis. Mixing axes breaks the conservation statement.
Ikhadi 298
Umbuzo
For a chosen object or system about an axis fixed in an inertial frame, what does signed area under its net-external-torque-versus-time graph represent?
Impendulo
Angular impulse, equal to that object or system's ΔL about the axis. Use the graph's signed-axis convention. The area has units N·m·s, equivalent to kg·m²/s.
Ikhadi 299
Umbuzo
Why can static friction act on a rigid object rolling without slipping on a stationary rigid surface without necessarily dissipating mechanical energy?
Impendulo
The contact point is instantaneously at rest relative to the surface, so there is no sliding. Static friction can still supply the torque needed for rolling.
Ikhadi 300
Umbuzo
For a satellite whose mass is negligible beside a fixed central mass M, what is its speed in a gravity-only circular orbit at center-to-center radius r?
Impendulo
v = √(GM/r). Gravity supplies the inward net force.
Ikhadi 301
Umbuzo
A chosen system's included mass co-rotates with one common angular velocity before and after a change. If its rotational inertia about an axis fixed in an inertial frame doubles while net external torque about that axis is negligible, what happens to its angular speed?
Impendulo
It halves. Because all included mass shares one angular velocity in each state, L = Iω applies. With the same axis and sign convention, angular-momentum conservation gives I_iω_i = I_fω_f.
Ikhadi 302
Umbuzo
For a rigid system rotating about an axis fixed in an inertial frame, what does signed area under its net-external-torque-versus-angular-position graph represent when angle is in radians?
Impendulo
Net rotational work, equal to the system's change in rotational kinetic energy. Torque and angular position must use the same signed axis.
Ikhadi 303
Umbuzo
Why can't the rolling condition alone prove that friction points uphill or downhill?
Impendulo
Friction direction depends on the tendency to slip and the applied forces or torques. Solve the dynamics instead of guessing from motion.
Ikhadi 304
Umbuzo
A satellite of mass m, negligible beside a fixed central mass M, follows a circular orbit at center-to-center radius r under gravity alone. What is its total mechanical energy?
Impendulo
E = -GMm/(2r). A larger circular orbit has greater, less-negative energy even though its speed is lower.
Ikhadi 305
Umbuzo
A spinning student pulls masses closer to an axis fixed in the lab's inertial frame while net external torque about that axis is negligible. Why does angular speed increase?
Impendulo
Rotational inertia decreases while angular momentum stays constant. Therefore Iω remains constant by increasing ω.
Ikhadi 306
Umbuzo
What makes simple harmonic motion a special kind of periodic motion?
Impendulo
Its restoring force or torque is proportional to displacement and points toward equilibrium. Periodic motion alone does not guarantee this relationship.
Ikhadi 307
Umbuzo
What does the amplitude of an SHM displacement graph represent?
Impendulo
The maximum distance from equilibrium. It is nonnegative even though displacement alternates sign.
Ikhadi 308
Umbuzo
How are period and frequency related?
Impendulo
T = 1/f. Period is seconds per cycle; frequency is cycles per second, measured in hertz.
Ikhadi 309
Umbuzo
What is the period of a mass m on an ideal spring of constant k when spring mass and damping are negligible?
Impendulo
T = 2π√(m/k). The motion must stay in the spring's linear SHM range.
Ikhadi 310
Umbuzo
For one-dimensional SHM, what is the equilibrium position?
Impendulo
The position where the restoring force or torque—and therefore acceleration along the SHM coordinate—is zero. A stable equilibrium produces a restoring response after a small displacement.
Ikhadi 311
Umbuzo
How far apart in phase are displacement and velocity in SHM?
Impendulo
One-quarter cycle. Velocity reaches an extremum when displacement crosses zero.
Ikhadi 312
Umbuzo
When can a simple pendulum be modeled as SHM?
Impendulo
For small angular displacements. Then the restoring torque is approximately proportional to angular displacement.
Ikhadi 313
Umbuzo
An oscillator completes 12 cycles in 6 s. What are its frequency and period?
Impendulo
f = 2 Hz and T = 0.5 s. Frequency is cycles per time, and period is its reciprocal.
Ikhadi 314
Umbuzo
For a horizontal ideal spring oscillator, what is potential energy at displacement x from its relaxed equilibrium length when U_s = 0 there?
Impendulo
U_s = ½kx². It has the same value at +x and -x.
Ikhadi 315
Umbuzo
At the equilibrium position of SHM, is the oscillator necessarily at rest?
Impendulo
No. The restoring force or torque and acceleration along the SHM coordinate are zero there, but speed is usually greatest.
Ikhadi 316
Umbuzo
How does a spring oscillator's period change if k becomes four times as large?
Impendulo
The period is halved. T is proportional to 1/√k.
Ikhadi 317
Umbuzo
How are acceleration and displacement related along the SHM coordinate?
Impendulo
a = -ω²x, where ω = 2πf is the oscillation's angular frequency. Here ω describes the oscillator's phase rate, not a rigid body's rotational angular velocity. The acceleration component along the SHM coordinate points toward equilibrium.
Ikhadi 318
Umbuzo
For a horizontal ideal spring oscillator with amplitude A, what is total mechanical energy when U_s = 0 at the relaxed equilibrium length?
Impendulo
E = ½kA². It stays constant when dissipative effects are negligible.
Ikhadi 319
Umbuzo
In a small-angle pendulum, where are speed and gravitational potential energy greatest?
Impendulo
Speed is greatest at the bottom; gravitational potential energy is greatest at the turning points. Energy trades between those forms.
Ikhadi 320
Umbuzo
How can frequency be read from an oscillation-versus-time graph?
Impendulo
Measure the time between repeating equivalent points to find T, then use f = 1/T. Adjacent peaks are one period apart.
Ikhadi 321
Umbuzo
Why does an ideal mass–spring oscillator exhibit SHM?
Impendulo
Its net restoring force is F_net = -kx, where x is displacement from equilibrium. The force is proportional to displacement and points back toward equilibrium.
Ikhadi 322
Umbuzo
A horizontal ideal spring has k = 50 N/m and amplitude 0.20 m. With U_s = 0 at equilibrium, what is the oscillator's total energy?
Impendulo
1 J. E = ½(50)(0.20²).
Ikhadi 323
Umbuzo
At maximum positive displacement in SHM, what are velocity and acceleration?
Impendulo
Velocity is zero; acceleration has maximum magnitude toward equilibrium. With positive displacement, acceleration is negative.
Ikhadi 324
Umbuzo
How does a spring oscillator's period change if its mass becomes four times as large?
Impendulo
The period doubles. T is proportional to √m.
Ikhadi 325
Umbuzo
Why isn't uniform circular motion itself one-dimensional SHM?
Impendulo
The object travels around a circle, not back and forth along one line. Its projection onto a diameter does follow SHM.
Ikhadi 326
Umbuzo
For the same ideal oscillator, how does total SHM energy change if amplitude doubles while k or mω² stays fixed?
Impendulo
It becomes four times as large. Under those fixed system parameters, total energy is proportional to A².
Ikhadi 327
Umbuzo
In one-dimensional SHM, what are speed and acceleration along the SHM coordinate at equilibrium?
Impendulo
Speed is maximum, while acceleration along the SHM coordinate is zero. The restoring force or torque vanishes there.
Ikhadi 328
Umbuzo
Does changing amplitude change the period of an ideal spring oscillator or small-angle pendulum?
Impendulo
No within the ideal SHM model. The period depends on system parameters, not amplitude.
Ikhadi 329
Umbuzo
How is maximum speed related to amplitude and angular frequency in SHM?
Impendulo
v_max = ωA. Maximum speed occurs at equilibrium.
Ikhadi 330
Umbuzo
For a horizontal ideal spring oscillator, how can kinetic energy at displacement x from equilibrium be found for amplitude A?
Impendulo
K = ½k(A² - x²). Subtract spring potential energy from the constant total.
Ikhadi 331
Umbuzo
How far apart in phase are displacement and acceleration in SHM?
Impendulo
Half a cycle, or 180°. When displacement is nonzero, acceleration has the opposite sign; at equilibrium, both are zero.
Ikhadi 332
Umbuzo
What is the period of a small-angle simple pendulum of length L when damping is negligible?
Impendulo
T = 2π√(L/g). The simple-pendulum model uses a point-like bob on a light, inextensible string with a fixed support; bob mass doesn't affect the period.
Ikhadi 333
Umbuzo
If x(t) is at a positive maximum at t = 0, what qualitative pattern follows over one cycle?
Impendulo
It crosses equilibrium moving negative at T/4, reaches negative maximum at T/2, returns through equilibrium at 3T/4, and reaches maximum positive displacement at T.
Ikhadi 334
Umbuzo
At equilibrium, how are a horizontal ideal spring oscillator's energies divided?
Impendulo
Kinetic energy is maximum and spring potential energy is minimum. With x measured from equilibrium, U_s = 0 at x = 0.
Ikhadi 335
Umbuzo
An SHM object is at negative displacement and moving toward equilibrium. What signs do velocity and acceleration have if positive is right?
Impendulo
Both are positive. Motion and restoring acceleration point right toward equilibrium.
Ikhadi 336
Umbuzo
How does a pendulum's period change if its length becomes nine times as large?
Impendulo
The period triples. T is proportional to √L.
Ikhadi 337
Umbuzo
If SHM starts at maximum positive displacement, what equation gives its position?
Impendulo
x(t) = A cos(2πft). A is amplitude, f is frequency, and t is elapsed time.
Ikhadi 338
Umbuzo
What feature would rule out ideal SHM in a force-versus-displacement-from-equilibrium graph?
Impendulo
A restoring-force relationship that is not a straight line through the origin over the motion's range. Ideal SHM needs F ∝ -x.
Ikhadi 339
Umbuzo
At a horizontal ideal spring oscillator's turning points, how are kinetic and spring potential energy divided?
Impendulo
Kinetic energy is zero and spring potential energy is maximum. The object momentarily stops at |x| = A.
Ikhadi 340
Umbuzo
For the same ideal spring with negligible damping and spring mass, which graph can determine k from measured periods and attached masses?
Impendulo
Graph T² versus m. For T = 2π√(m/k), the slope is 4π²/k.
Ikhadi 341
Umbuzo
What makes a substance a fluid?
Impendulo
It deforms continuously under a shear force and takes the shape of its container. Liquids and gases are fluids.
Ikhadi 342
Umbuzo
What is mass density?
Impendulo
Mass per volume: ρ = m/V. Its SI unit is kg/m³.
Ikhadi 343
Umbuzo
For pressure that is uniform over a surface patch, how is it related to normal force and area?
Impendulo
P = F_perpendicular/A. Pressure is a scalar field even though the contact force has direction.
Ikhadi 344
Umbuzo
What is volume flow rate?
Impendulo
Volume passing a cross-section per time: Q = ΔV/Δt. Its SI unit is m³/s.
Ikhadi 345
Umbuzo
What is the buoyant-force magnitude on an object immersed in a static fluid whose density is uniform over the displaced volume?
Impendulo
The weight of the displaced fluid: F_B = ρ_fluid gV_displaced. Here ρ_fluid is the uniform density over that volume.
Ikhadi 346
Umbuzo
What conditions support the basic Bernoulli model used here?
Impendulo
Steady, incompressible, nonviscous flow along the compared flow path, with a completely filled pipe unless stated otherwise. Incompressible means a moving fluid element's density stays effectively constant. Pumps or major dissipative effects require extra terms.
Ikhadi 347
Umbuzo
Under the ideal model, how does average density predict whether a free object floats or sinks?
Impendulo
It floats if its average density is less than the fluid's and sinks if it is greater. Equal average density gives neutral buoyancy when fully submerged; assume no support or other external force.
Ikhadi 348
Umbuzo
How are volume flow rate, cross-sectional area, and average fluid speed normal to that area related?
Impendulo
Q = Av. This gives the volume crossing a completely filled pipe section per time.
Ikhadi 349
Umbuzo
How does a static fluid exert force on a surface?
Impendulo
Many particle–surface interactions produce a net force perpendicular to the surface. A static fluid does not exert a tangential shear force.
Ikhadi 350
Umbuzo
How does pressure change with depth in a static uniform fluid?
Impendulo
It increases by ΔP = ρgΔh. Greater depth means more fluid weight above each unit area.
Ikhadi 351
Umbuzo
What force balance holds for an object floating at rest when buoyancy and weight are its only vertical forces?
Impendulo
F_B = mg. The object's weight equals the weight of the fluid it displaces.
Ikhadi 352
Umbuzo
What is the continuity equation for steady incompressible flow in one filled pipe?
Impendulo
A₁v₁ = A₂v₂. The same volume flow rate passes each cross-section.
Ikhadi 353
Umbuzo
Why does a static fluid produce an upward buoyant force?
Impendulo
Pressure is greater on the object's lower surfaces than on its upper surfaces. The vertical pressure forces do not cancel.
Ikhadi 354
Umbuzo
What is the absolute pressure at depth h below the open surface of a static, uniform liquid?
Impendulo
P_abs = P_atm + ρgh. ρgh is the gauge pressure from the liquid column.
Ikhadi 355
Umbuzo
Immediately after a fully submerged object is released in a static, uniform ideal fluid, which way does it accelerate if its average density exceeds the fluid density and only weight and buoyancy act?
Impendulo
Downward. Weight exceeds buoyant force, so the initial net force and acceleration point downward.
Ikhadi 356
Umbuzo
Water's average speed normal to a 0.020 m² pipe cross-section is 3 m/s. What is the volume flow rate?
Impendulo
0.060 m³/s. Q = Av = 0.020×3.
Ikhadi 357
Umbuzo
What does the slope of a mass-versus-volume graph represent for one uniform material?
Impendulo
Density. Since m = ρV, the line's slope is ρ.
Ikhadi 358
Umbuzo
How do gauge pressure and absolute pressure differ?
Impendulo
Gauge pressure is measured relative to atmospheric pressure; absolute pressure is measured relative to vacuum. P_abs = P_atm + P_gauge.
Ikhadi 359
Umbuzo
For a fully submerged rigid object in a static, incompressible, uniform fluid, does buoyant force increase with depth?
Impendulo
No. Displaced volume, fluid density, and g stay constant, so F_B stays constant despite higher absolute pressure.
Ikhadi 360
Umbuzo
For steady incompressible flow in a filled pipe, what happens to speed if cross-sectional area halves?
Impendulo
It doubles. Continuity keeps Av constant.
Ikhadi 361
Umbuzo
When does a fluid element's velocity change?
Impendulo
Its velocity changes when a nonzero net force acts on it. Pressure forces and gravity can contribute to that net force.
Ikhadi 362
Umbuzo
For steady, incompressible, nonviscous flow along the same flow path, what does Bernoulli's equation express?
Impendulo
Conservation of mechanical energy per unit volume. Along that flow path, P + ½ρv² + ρgy stays constant under the stated conditions.
Ikhadi 363
Umbuzo
For a uniform object floating at rest in a uniform-density fluid with buoyancy and weight as its only vertical forces, what fraction of its volume is submerged?
Impendulo
V_sub/V_object = ρ_object/ρ_fluid. A less-dense object floats with a smaller fraction submerged.
Ikhadi 364
Umbuzo
For steady incompressible flow in a filled pipe, what happens to speed if pipe radius halves?
Impendulo
It becomes four times as large. Area is proportional to radius squared.
Ikhadi 365
Umbuzo
What does Pascal's principle say for a confined incompressible fluid at rest?
Impendulo
An applied pressure change is transmitted throughout the fluid. The same pressure change acts at every connected point.
Ikhadi 366
Umbuzo
In a uniform static fluid, what does the slope of gauge pressure versus depth represent?
Impendulo
ρg. For known g, the slope can determine fluid density.
Ikhadi 367
Umbuzo
Immediately after a fully submerged object is released in a static, uniform ideal fluid, which way does it accelerate if its average density is less than the fluid density and only weight and buoyancy act?
Impendulo
Upward. Buoyant force exceeds weight, so the initial net force and acceleration point upward.
Ikhadi 368
Umbuzo
For steady incompressible flow in a filled pipe, area narrows from 0.040 m² to 0.010 m². If initial speed is 2 m/s, what is final speed?
Impendulo
8 m/s. Continuity gives v₂ = A₁v₁/A₂.
Ikhadi 369
Umbuzo
What physical quantity does each term in P + ½ρv² + ρgy share?
Impendulo
Energy per unit volume, equivalent to pressure. Every term uses units of pascals.
Ikhadi 370
Umbuzo
In one static fluid of uniform density, what experimental graph could test F_B = ρ_fluid gV_displaced?
Impendulo
Graph measured buoyant force versus displaced volume. A line with slope near ρ_fluid g supports the model.
Ikhadi 371
Umbuzo
A uniform object of density 750 kg/m³ floats at rest in uniform-density water of density 1000 kg/m³, with buoyancy and weight as its only vertical forces. What fraction is submerged?
Impendulo
0.75, or 75%. Use the density ratio for floating equilibrium.
Ikhadi 372
Umbuzo
A main pipe splits into two outlets during steady incompressible flow. What flow-rate relation holds?
Impendulo
Incoming flow rate equals the sum of outgoing flow rates. Q_in = Q_out,1 + Q_out,2.
Ikhadi 373
Umbuzo
For steady, incompressible, nonviscous efflux with negligible losses, what is Torricelli's speed for an opening a vertical distance h below a large open surface?
Impendulo
v = √(2gh). Both locations are open to atmospheric pressure, and the large surface makes the upper-fluid speed negligible.
Ikhadi 374
Umbuzo
Why does the same force create more pressure on a smaller area?
Impendulo
Pressure is inversely proportional to area for fixed perpendicular force. Concentrating the force raises F/A.
Ikhadi 375
Umbuzo
A sample has mass 0.60 kg and volume 2.0×10⁻⁴ m³. What is its density?
Impendulo
3.0×10³ kg/m³. Divide mass by volume.
Ikhadi 376
Umbuzo
What conservation law underlies the continuity equation for incompressible flow?
Impendulo
Conservation of mass. Constant density turns equal mass flow into equal volume flow.
Ikhadi 377
Umbuzo
An immersed object rests on a scale that exerts an upward support force. If weight, buoyancy, and that support are its only vertical forces, with mg ≥ F_B, how is apparent weight related to buoyant force?
Impendulo
N = mg - F_B. Here N is the upward scale-force magnitude. The fluid supports part of the object's weight, so the scale reading is no greater than its weight under the stated condition.
Ikhadi 378
Umbuzo
What is the SI unit of pressure?
Impendulo
The pascal, Pa. One pascal equals 1 N/m².
Ikhadi 379
Umbuzo
How do pressures compare at the same horizontal level in one connected static fluid?
Impendulo
They are equal. Container shape does not change pressure at a fixed elevation.
Ikhadi 380
Umbuzo
What does specific gravity compare?
Impendulo
A substance's density with water's density. It is a dimensionless ratio, commonly ρ_substance/ρ_water.
Ikhadi 381
Umbuzo
How could collecting outflow test a volume flow rate predicted from area and average normal speed?
Impendulo
Measure collected volume over a timed interval and compare ΔV/Δt with Av. Repeat trials and include volume and timing uncertainty.
Ikhadi 382
Umbuzo
How does the particle model distinguish a fluid from a rigid solid?
Impendulo
Fluid particles can rearrange and flow past one another. A rigid solid resists sustained shape change.
Ikhadi 383
Umbuzo
At equal height along the same flow path in steady, incompressible, nonviscous flow, how are pressure and speed related?
Impendulo
The faster region has lower static pressure. Along that flow path at equal height, P + ½ρv² remains constant.
Ikhadi 384
Umbuzo
A fully submerged object displaces 0.020 m³ of static water. Using ρ = 1000 kg/m³ and g = 10 m/s², what is F_B?
Impendulo
200 N. F_B = ρgV = 1000×10×0.020.
Ikhadi 385
Umbuzo
Why can a steel ship float even though steel is denser than water?
Impendulo
Its hollow shape makes the ship's overall average density less than water. It displaces enough water for buoyant force to balance weight.
Ikhadi 386
Umbuzo
How does an ideal hydraulic lift with a confined incompressible fluid at rest multiply force?
Impendulo
Equal pressure change gives F₁/A₁ = F₂/A₂. The larger-area piston produces the larger force.
Ikhadi 387
Umbuzo
For steady, incompressible, nonviscous efflux with negligible losses, what graph can test Torricelli's relation while fluid head h varies?
Impendulo
Graph v² versus h. With both locations open to atmospheric pressure and upper-surface speed negligible, the model predicts slope 2g.
Ikhadi 388
Umbuzo
What does incompressible mean in the introductory ideal-fluid model?
Impendulo
A fluid element's density stays effectively constant as it moves. Its volume does not appreciably shrink under pressure changes.
Ikhadi 389
Umbuzo
At two points along the same flow path in steady, incompressible, nonviscous flow, how are pressure and height related when speed is equal?
Impendulo
Pressure is lower at the higher point. P + ρgy remains constant.
Ikhadi 390
Umbuzo
How can water displacement measure an irregular solid's volume?
Impendulo
Submerge it fully and measure the increase in displaced-water volume. The volume change equals the submerged solid's volume if no water enters it.
Ikhadi 391
Umbuzo
Two equal-volume samples have densities ρ and 3ρ. How do their masses compare?
Impendulo
The denser sample has three times the mass. From m = ρV, mass scales with density at fixed volume.
Ikhadi 392
Umbuzo
How can scale readings in air and water determine buoyant force?
Impendulo
Subtract the immersed scale reading from the air reading. When the object is at rest and air buoyancy is negligible, the decrease equals the liquid's buoyant force.
Ikhadi 393
Umbuzo
Static water has ρ = 1000 kg/m³. Using g = 10 m/s², what gauge pressure is 3 m below its open surface?
Impendulo
30,000 Pa. P_gauge = ρgh = 1000×10×3.
Ikhadi 394
Umbuzo
During steady incompressible outflow, why can a large tank's top-surface speed be neglected compared with outlet speed?
Impendulo
The tank's surface area is much larger than the outlet area. Continuity then makes the top-surface speed much smaller.
Ikhadi 395
Umbuzo
For a chosen fluid element in a horizontal region, what can a pressure difference do?
Impendulo
It creates a net pressure force from higher pressure toward lower pressure and can accelerate the element by Newton's second law. Other forces must also be included when they matter.
Ikhadi 396
Umbuzo
How can buoyancy measurements in a static fluid of known uniform density determine an irregular object's volume?
Impendulo
Measure buoyant force while the object is fully submerged, then use V = F_B/(ρ_fluid g). The fluid density must be uniform over the displaced volume.
Ikhadi 397
Umbuzo
A 200 N perpendicular force acts on area 0.040 m². What pressure does it create?
Impendulo
5,000 Pa. P = F/A = 200/0.040.
Ikhadi 398
Umbuzo
Why doesn't a hydraulic lift multiply energy?
Impendulo
The large-force piston moves a shorter distance. Ideally, input work equals output work.
Ikhadi 399
Umbuzo
A large open tank has steady, incompressible, nonviscous efflux with negligible losses. Using g = 10 m/s², what speed leaves an opening 5 m below the surface when upper-surface speed is negligible?
Impendulo
10 m/s. Both locations are at atmospheric pressure, so v = √(2gh) = √100.
Ikhadi 400
Umbuzo
An object floats first in water and then in a denser liquid. How does its submerged fraction change?
Impendulo
It decreases in the denser liquid. Less displaced volume is needed to provide the same buoyant force.

An orange sphere traces an orbital path between a wave, a rotating disc, and a fluid ripple on a dark grid.

amakhadi angu-400