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.

Mwandishi Open Study Contributor

Kuhusu fungu hili

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.

Kadi za fungu hili

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

kadi 400