The graph shows the angular momentum L of a rigid system as a function of time t. Which of the following statements about the torque exerted on the system is supported by the graph?

The torque increases in magnitude and is in the opposite direction of the angular momentum.

The torque decreases in magnitude and is in the same direction as the angular momentum.

The torque decreases in magnitude and is in the opposite direction of the angular momentum.

The torque increases in magnitude and is in the same direction as the angular momentum.

A horizontal platform with rotational inertia I p is spinning about a central axis with negligible friction, as shown. A ball of clay with rotational inertia about its center I c , where I c < I p , is dropped onto, and sticks to, the center of the platform. Which of the following claims about the magnitude of the angular impulse exerted on the platform by the clay is true?

It is equal to the magnitude of the angular impulse exerted on the clay by the platform.

It is greater than the magnitude of the angular impulse exerted on the clay by the platform.

It is less than the magnitude of the angular impulse exerted on the clay by the platform, but greater than zero.

The impulse exerted on each object cannot be compared without knowing the relative masses of the clay and platform.

In the setup shown, a hollow plastic pipe can spin with negligible friction on an axle at the center of the pipe, as shown. Two solid cylinders are placed inside the pipe at the locations shown. The pipe is given an initial angular speed, and the pipe-cylinders system rotates about the axle. As the system rotates, the cylinders slide toward the ends of the pipe. Which of the following correctly indicates how the angular speed of the system changes, if at all, as the cylinders slide and provides a valid justification?

(A) The angular speed decreases, because the rotational inertia of the system increases.

(B) The angular speed decreases, because the rotational inertia of the system decreases.

(C) The angular speed remains constant, because angular momentum is conserved.

(D) The angular speed remains constant, because no external torque is exerted on the system.

A rod is initially at rest on a horizontal surface and free to rotate about its left end, as shown. A disk slides along the surface toward the right end of the rod in the direction indicated in the figure. When the disk reaches the rod, it sticks to the rod, and the disk and the rod rotate together about the left end of the rod. Friction forces, except those between the disk and the rod, are negligible. Which of the following correctly states whether the angular momentum of the disk-rod system changes as a result of the collision, and provides the best justification for the statement?

No, because the torques exerted on the rod and the disk are internal to the system.

Yes, because the rod will begin rotating and the angular momentum will increase.

Yes, because only one component of the disk’s velocity will contribute to the system’s angular momentum and the angular momentum will decrease.

No, because angular momentum of all systems is always constant.

A puck slides toward the right with a constant velocity across a smooth surface toward a bar that is free to rotate about a pivot at one end, as shown in the top view figure. The puck collides with and sticks to the bar, and the puck and bar rotate together about the bar’s pivot. Which of the following statements correctly describes the change in angular momentum of the puck and the bar about the pivot during the collision?

The decrease in the angular momentum of the puck is equal to the increase in the angular momentum of the bar.

The decrease in the angular momentum of the puck is less than the increase in the angular momentum of the bar.

The decrease in the angular momentum of the puck is greater than the increase in the angular momentum of the bar.

The decrease in the angular momentum of the puck could be less than, equal to, or greater than the increase in the angular momentum of the bar, depending on the relative rotational inertias.

A student sits on a platform that can rotate with negligible friction. The student holds weights out with extended arms and the teacher gives the student a push to cause the student to begin spinning on the platform with constant angular velocity. While spinning, the student pulls the weights in toward the student’s body. Which of the following correctly describes how the angular momentum of the student-weights system changes, if at all, when the weights are pulled in and provides a valid justification?

The angular momentum remains constant, because no external net torque is exerted on the system.

The angular momentum increases, because the student transfers energy to the weights.

The angular momentum increases, because the angular speed of the student will increase.

The angular momentum remains constant, because no energy is transferred to the system.

Which of the following correctly compares the escape speeds v esc,1 and v esc,2 of Satellite 1 and Satellite 2, respectively?

The comparison of the escape speeds cannot be made without knowing the masses of the satellites.

A satellite has speed v when it is at point P, which is located outside Earth’s atmosphere a distance R from Earth’s center. The satellite then fires its thrusters and eventually reaches point Q, a distance 5R from Earth’s center, where the satellite again has speed v. The total mechanical energy of the satellite-Earth system is E P when the satellite is at point P, and E Q when the satellite is at point Q. Which of the following correctly compares E Q to E P , and provides a valid justification?

E Q > E P because the gravitational potential energy increases with increasing distance from Earth’s center.

E Q = E P because the thruster exerts a force equal in magnitude and opposite in direction to the gravitational force exerted by Earth.

E Q = E P because the satellite has the same kinetic energy at both points.

E Q > E P because the total mechanical energy of the system is proportional to the distance between the satellite and Earth’s center.

Three identical satellites orbit Earth in the orbits shown in the figure. Satellite 1 has a circular orbit of radius R, Satellite 2 has a circular orbit of radius 2R, and Satellite 3 has an elliptical orbit such that the distance between Satellite 3 and the center of Earth varies between R and 2R. Let v₁,max, v₂,max, and v₃,max be the maximum speeds of Satellites 1, 2, and 3 in their respective orbits. Which of the following correctly compares v₁,max, v₂,max, and v₃,max?

(B) v₃,max > v₁,max > v₂,max

(A) v₁,max > v₃,max > v₂,max

(C) v₃,max > v₂,max > v₁,max

(D) v₂,max > v₃,max > v₁,max

Satellites 1 and 2, with masses m and 2m, respectively, are in circular orbits around a planet at the same altitude h, as shown. Would each satellite require the same speed to escape the planet’s gravitational pull? Why or why not?

Yes, because the escape speed does not depend on the masses of the satellites.

Yes, because both satellite-planet systems have the same total mechanical energy.

No, because Satellite 2 has a larger amount of total mechanical energy so needs less energy to escape.

No, because Satellite 1 requires less energy to escape because it has a smaller mass than Satellite 2.

A satellite is in an elliptical orbit around Earth, as shown. Which of the following indicates whether the torque on the satellite is zero or nonzero throughout its motion, and provides a valid justification?

Zero, because the lever arm of the gravitational force on the satellite is always zero

Zero, because the speed of the satellite is constant

Nonzero, because the velocity of the satellite sometimes has a nonzero radial component

Nonzero, because the magnitude of the gravitational force changes throughout the orbit

A block and a hoop, both having the same mass, are released from rest at equal heights H above the floor on identical rough tracks, as shown. Both objects move down the track, with the block sliding and the hoop rolling without slipping. Each object then moves up a short, curved ramp and is launched vertically upward. Each object’s center of mass comes to rest momentarily at a height $$\frac{H}{2}$$ above the floor. A student claims that the total mechanical energies of the block-Earth system and the hoop-Earth system are equal when the centers of mass of the objects are momentarily at rest at height $$\frac{H}{2}$$ . Is the student’s claim correct? Why or why not?

No, because when the center of mass of the hoop is momentarily at rest it has nonzero rotational kinetic energy.

Yes, because both systems start with the same gravitational potential energy.

Yes, because both objects have zero kinetic energy when their centers of mass are momentarily at rest.

No, because the work done by gravity is not the same for both objects.

A solid cylinder with known radius is rolling while slipping along a horizontal surface, as shown. The center of mass of the cylinder is moving to the right and slowing down, and the cylinder is rotating in a counterclockwise direction. At the instant shown, the speed of the center of mass of the cylinder is v cm and the angular speed of the cylinder is ω. Can the relationship between v cm and ω be determined? Why or why not?

No, because when an object is slipping, the motion of the center of mass and the rotational motion of the object are not related.

Yes, because the linear acceleration of the center of mass is related to the angular acceleration by a cm = rα.

No, because the friction force dissipates an unknown amount of energy from the cylinder-surface system.

One end of a string of negligible mass is wrapped around a disk and the other end is attached to a ceiling, as shown. The disk is released from rest at position A and the string does not slip on the disk. When the disk reaches position B, the absolute value of the change in the gravitational potential energy of the disk-Earth system is ΔU. Which of the following correctly compares the total kinetic energy and the rotational kinetic energy of the disk to ΔU?

Total Kinetic Energy: Equal to ΔU, Rotational Kinetic Energy: Less than ΔU

Total Kinetic Energy: Equal to ΔU, Rotational Kinetic Energy: Equal to ΔU

Total Kinetic Energy: Less than ΔU, Rotational Kinetic Energy: Equal to ΔU

Total Kinetic Energy: Less than ΔU, Rotational Kinetic Energy: Less than ΔU

A disk is released from rest from the top of a ramp and rolls to the bottom without slipping. A sphere with the same mass and radius as the disk, but with a smaller rotational inertia, is also released from rest at the top of the ramp and rolls to the bottom without slipping. K D and K S are the total kinetic energy of the disk and sphere, respectively, at the bottom of the ramp. How do K D and K S compare, and why?

K D = K S because the gravitational force does equal work on the sphere and the disk as they roll down the ramp.

K D > K S because the sphere will gain less rotational kinetic energy.

K D > K S because the sphere has a greater acceleration and therefore has less time to gain kinetic energy.

K D = K S because both the sphere and disk accelerate at the same rate.

A hoop is released from rest at the top of Ramp A and rolls down the ramp without slipping. When the hoop reaches the bottom of Ramp A, it has translational kinetic energy K tA . The hoop is then released from rest at the top of Ramp B, which has the same height and shape as Ramp A, but there is negligible friction between the hoop and Ramp B, so the hoop slides down Ramp B without rolling. When the hoop reaches the bottom of Ramp B, it has translational kinetic energy K tB . Which of the following correctly compares K tB and K tA ?

The comparison cannot be made without knowing the coefficient of static friction between the hoop and Ramp A.

A solid sphere and an ice cube of equal mass are released from rest at the top of an incline, as shown. The sphere rolls down the incline without slipping, while the ice cube slides down the incline with negligible friction. Which of the following correctly indicates whether the sphere or the cube has the greater translational speed when it reaches the bottom of the incline, and provides a valid justification?

(C) The cube, because the cube’s kinetic energy will all be in the form of translational kinetic energy, while some of the sphere’s kinetic energy will be in the form of rotational kinetic energy.

(A) The sphere, because its rolling motion will contribute to its translational motion, while the cube does not have any rolling motion.

(B) The sphere, because work is done on the sphere by both gravity and friction, while only gravity does work on the cube.

(D) The cube, because none of the mechanical energy of the cube will be dissipated by friction, while some of the mechanical energy of the sphere will be dissipated by friction.

A sphere of mass m, radius r, and rotational inertia $$\frac{2}{5}mr^2$$ is released from rest at the top of a ramp of height h, as shown. The sphere rolls down the ramp without slipping and when it reaches the bottom of the ramp, the sphere has rotational kinetic energy $$K_{r1}$$ and angular speed $$\omega_1$$ . A second sphere of the same radius but with mass 2m is released from rest from the same location as the first sphere. The second sphere rolls down the ramp without slipping and when it reaches the bottom of the ramp, the sphere has rotational kinetic energy $$K_{r2}$$ and angular speed $$\omega_2$$ . Which of the following correctly compares $$K_{r2}$$ to $$K_{r1}$$ and $$\omega_2$$ to $$\omega_1$$ ?

C. $$K_{r2} > K_{r1}$$ , $$\omega_2 = \omega_1$$

A. $$K_{r2} = K_{r1}$$ , $$\omega_2 = \omega_1$$

B. $$K_{r2} = K_{r1}$$ , $$\omega_2 > \omega_1$$

D. $$K_{r2} > K_{r1}$$ , $$\omega_2 > \omega_1$$

An asteroid is moving through deep space far from any other objects. The linear velocity of the center of mass of the asteroid is constant and the asteroid is rotating about its center of mass with constant angular velocity. Which of the following statements correctly describe the rotational and translational kinetic energy of the asteroid?

The rotational kinetic energy can be less than, equal to, or greater than the translational kinetic energy.

The rotational kinetic energy must be less than the translational kinetic energy.

The rotational kinetic energy must be equal to the translational kinetic energy.

The rotational kinetic energy must be greater than the translational kinetic energy.

AP Physics 1 - Unit 6

Authored by JOSHUA RIDENOUR

Science

11th Grade

NGSS covered

Used 6+ times

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

8 kg · m^2/s

12 kg · m^2/s

16 kg · m^2/s

20 kg · m^2/s

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The graph shows the net torque exerted on a rigid object as a function of time. Which of the following claims about the angular impulse delivered to the object during the interval shown in the graph is true?

The angular impulse is zero.

The angular impulse is less than zero.

The angular impulse is greater than zero.

The angular impulse could be greater than or less than zero depending on the initial direction of rotation.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Two forces of equal magnitude are exerted at separate times to a board that is initially at rest and free to rotate about an axis at one end of the board, as shown in the figures. In Figure 1, a force of magnitude F is exerted perpendicular to the board at the center of the board for a time 2t, after which the board has a final angular momentum about the axis of magnitude L1. In Figure 2, the board is returned to rest at its initial position and a force of magnitude F is exerted at a constant angle to the board of 60° at the end of the board for time t, after which the board has a final angular momentum about the axis of magnitude L2. Which of the following is equal to the ratio L2 : L1?

(A) 1 : 1

(B) 1 : 2

(D) 1 : 4

The diagram shows an amusement park ride that consists of a car of mass m connected to a motor by a rigid arm of length R. The motor spins the arm and the car moves in a vertical circle. In Figure 1, the car is at the bottom of the circle with a tangential velocity of magnitude v1. In Figure 2, the car has moved clockwise along the circle through an angle θ, and has tangential velocity of magnitude v2, where v2 > v1. Which of the following is equal to the change in angular momentum of the car about the rotation axis between Figure 1 and Figure 2?

mR(v2 − v1)

mgR(1 − cos θ)

mv2Rsin θ

A disk slides with constant velocity on a horizontal surface, as shown in the top-view figure. Friction forces between the disk and the surface are negligible. Which of the following statements correctly describes the angular momentum of the disk relative to Point P?

The angular momentum is constant and zero.

The angular momentum is constant and greater than zero.

The angular momentum decreases.

The angular momentum increases.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In an experiment, a puck slides toward the end of a rod that is free to rotate on a horizontal surface about a pivot at its left end, as shown in the top view figure. In each trial, the puck slides with constant speed v but the angle θ between the velocity vector and the rod is varied. The angular momentum L of the puck about the pivot immediately before the puck reaches the rod is calculated. Which of the following graphs could show L as a function of θ?

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

A horizontal platform is initially rotating about a vertical axis as shown in Figure 1. A stationary disk is dropped directly onto the center of the platform. A short time later, the disk and platform rotate together without slipping, as shown in Figure 2. How does the angular momentum of only the platform change, if at all, after the disk drops? What is a justification for your answer?

The angular momentum of the platform decreases. The top disk exerts a torque on the platform.

The angular momentum of the platform decreases. The potential energy of the platform-disk-Earth system decreases when the disk drops.

The angular momentum of the platform stays the same. Angular momentum is a conserved quantity.

The angular momentum of the platform stays the same. The torques that the disk and platform exert on each other are equal in magnitude but opposite in direction.

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