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.

مصنف Open Study Contributor

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مطالعہ شروع کرنے کے لیے Nibomo کھلے گا۔

ڈیک کی تفصیلات

کارڈز: 400 کارڈز
ورژن: 3
شائع شدہ: 26 اگست، 2026
آخری بار اپ ڈیٹ ہوا: 10 ستمبر، 2026
لائسنس: Common knowledge · CC0 1.0
ہدف سیکھنے والوں کی زبانیں: en
مضمون: Physics
سطح: AP Physics 1
ٹیگز: algebra-based-physics-1, unit-1, unit-2, unit-3, unit-4, unit-5, unit-6, unit-7, unit-8

ملتے جلتے ڈیک

اس ڈیک کے بارے میں

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.

اس ڈیک کے کارڈز

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

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