Quiz about AP Physics 1: Chapter 8: Rotational Equilibrium and Dynamics

Question 1

For the wheel-and-axle system shown above, which of the following expresses the condition required for the system to be in static equilibrium?

Accepted Answer

$$am_1=bm_2$$

Answer

$$m_1=m_2$$

Answer

$$am_2=bm_1$$

Answer

$$a=b$$

Question 2

A bowling ball of mass M and radius R. whose moment of inertia about its center is $$\frac{2}{5}MR^2$$ , rolls without slipping along a level surface at speed v. The maximum vertical height to which it can roll if it ascends an incline is

Accepted Answer

$$\frac{7v^2}{10g}$$

Answer

$$\frac{v^2}{5g}$$

Answer

$$\frac{2v^2}{5g}$$

Answer

$$\frac{v^2}{2g}$$

Question 3

A sphere of mass M, radius r, and rotational inertia I is released from rest at the top of an inclined plane of height h as shown above.

If the plane is frictionless, what is the speed $$v_{cm}$$ , of the center of mass of the sphere at the bottom of the incline?

Accepted Answer

$$\sqrt[]{2gh}$$

Answer

$$\frac{2Mghr^2}{I}$$

Answer

$$\sqrt[]{\frac{2Mghr^2}{I}}$$

Answer

$$\sqrt[]{\frac{2Mghr^2}{I+Mr^2}}$$

Question 4

A sphere of mass M, radius r, and rotational inertia I is released from rest at the top of an inclined plane of height h as shown above.

If the plane has friction so that the sphere rolls without slipping, what is the speed $$v_{cm}$$ of the center of mass at the bottom of the incline?

Accepted Answer

$$\sqrt[]{\frac{2Mghr^2}{I+Mr^2}}$$

Answer

$$\sqrt[]{2gh}$$

Answer

$$\frac{2Mghr^2}{I}$$

Answer

$$\sqrt[]{\frac{2Mghr^2}{I}}$$

Question 5

A rod of negligible mass is pivoted at a point that is off-center, so that length $$l_1$$ is different from length $$l_2$$ . The figures above show two cases in which masses are suspended from the ends of the rod. In each case the unknown mass m is balanced by a known mass, $$M_1$$ or $$M_2$$ , so that the rod remains horizontal. What is the value of m in terms of the known masses?

Accepted Answer

$$\sqrt[]{M_1M_2}$$

Answer

$$M_1+M_2$$

Answer

$$\frac{1}{2}\left(M_1+M_2\right)$$

Answer

$$M_1M_2$$

Question 6

A system of two wheels fixed to each other is free to rotate about a frictionless axis through the common center of the wheels and perpendicular to the page. Four forces are exerted tangentially to the rims of the wheels, as shown above. The magnitude of the net torque on the system about the axis is:

Accepted Answer

2FR

Answer

FR

Answer

5FR

Answer

14FR

Question 7

A solid cylinder of mass m and radius R has a string wound around it. A person holding the string pulls it vertically upward, as shown above, such that the cylinder is suspended in midair for a brief time interval $$\Delta t$$ and its center of mass does not move. The tension in the string is T, and the rotational inertia of the cylinder about its axis is $$\frac{1}{2}MR^2$$ .

The net force on the cylinder during the time interval $$\Delta t$$ is:

Accepted Answer

zero

Answer

mg

Answer

T-mgR

Answer

mgR-T

Question 8

A solid cylinder of mass m and radius R has a string wound around it. A person holding the string pulls it vertically upward, as shown above, such that the cylinder is suspended in midair for a brief time interval $$\Delta t$$ and its center of mass does not move. The tension in the string is T, and the rotational inertia of the cylinder about its axis is $$\frac{1}{2}MR^2$$ .

The linear acceleration of the person's hand during the time interval $$\Delta t$$ is:

Accepted Answer

$$2g$$

Answer

$$\frac{2T}{m}$$

Answer

$$\frac{T}{m}$$

Answer

zero

Question 9

A block of mass $$m$$ is placed against the inner wall of a hollow cylinder of radius $$R$$ that rotates about a vertical axis with a constant angular velocity $$\omega$$ , as shown above. In order for friction to prevent the mass from sliding down the wall, the coefficient of static friction $$\mu$$ between the mass and the wall must satisfy which of the following inequalities?

Accepted Answer

$$\mu\ge\frac{g}{\omega^2R}$$

Answer

$$\mu\ge\frac{\omega^2R}{g}$$

Answer

$$\mu\le\frac{g}{\omega^2R}$$

Answer

$$\mu\le\frac{\omega^2R}{g}$$

Question 10

The rigid body shown in the diagram above consists of a vertical support post and two horizontal crossbars with spheres attached. The masses of the spheres and the lengths of the crossbars are indicated in the diagram. The body rotates about a vertical axis along the support post with constant angular speed $$\omega$$ . If the masses of the support post and the crossbars are negligible, what is the ratio of the angular momentum of the two upper spheres to that of the two lower spheres?

Accepted Answer

1/8

Answer

2/1

Answer

1/2

Answer

1/4

Question 11

A long board is free to slide on a sheet of frictionless ice. As shown in the top view above, a skater skates to the board and hops onto one end, causing the board to slide and rotate. In this situation, which of the following occurs?

Accepted Answer

Linear momentum and angular momentum are both conserved.

Answer

Linear momentum is converted to angular momentum.

Answer

Rotational kinetic energy is conserved.

Answer

Translational kinetic energy is conserved.

Question 12

A disk sliding on a horizontal surface that has negligible friction collides with a rod that is free to move and rotate on the surface, as shown in the top view above. Which of the following quantities must be the same for the disk-rod system before and after the collision? Select two answers.

Accepted Answer

Linear Momentum

Accepted Answer

Angular Momentum

Answer

Kinetic Energy

Answer

Mechanical Energy

Question 13

A racing car is moving around the circular track of radius 300 meters shown above. At the instant when the car's velocity is directed due east, its acceleration is directed due south and has a magnitude of $$3\ \frac{m}{s^2}$$ . When viewed from above, the car is moving _____.

Accepted Answer

clockwise at $$30\ \frac{m}{s}$$

Answer

clockwise at $$10\ \frac{m}{s}$$

Answer

counterclockwise at $$30\ \frac{m}{s}$$

Answer

with constant velocity

Question 14

A spring has a force constant of $$100\ \frac{N}{m}$$ and an unstretched length of 0.07 m. One end is attached to a post that is free to rotate in the center of a smooth table, as shown in the top view above. The other end is attached to a 1 kg disc moving in uniform circular motion on the table, which stretches the spring by 0.03 m. Friction is negligible. What is the centripetal force on the disc?

Accepted Answer

3 N

Answer

0.3 N

Answer

10 N

Answer

30 N

Question 15

A figure of a dancer on a music box moves counterclockwise at constant speed around the path shown above. The path is such that the lengths of its segments, PQ, QR, RS, and SP, are equal. Arcs QR and SP are semicircles. Which of the following best represents the magnitude of the dancer's acceleration as a function of time t during one trip around the path, beginning at point P?

Accepted Answer

Question 16

One end of a string is fixed. An object attached to the other end moves on a horizontal plane with uniform circular motion of radius R and frequency f. The tension in the string is $$F_S$$ . If both the radius and frequency are doubled, the tension is _____.

Accepted Answer

increased eightfold

Answer

doubled

Answer

halved

Answer

unchanged

Answer

increased fourfold

Question 17

A wheel with rotational inertia $$I$$ is mounted on a fixed, frictionless axle. The angular speed $$\omega$$ of the wheel is increased from zero to $$\omega_f$$ in a time interval $$T$$ .

What is the average power input to the wheel during this time interval?

Accepted Answer

$$\frac{I\omega_f^2}{2T}$$

Answer

$$\frac{I\omega_f}{2T}$$

Answer

$$\frac{I\omega_f^2}{2T^2}$$

Answer

$$\frac{I^2\omega_f^2}{2T^2}$$

Question 18

A wheel with rotational inertia $$I$$ is mounted on a fixed, frictionless axle. The angular speed $$\omega$$ of the wheel is increased from zero to $$\omega_f$$ in a time interval $$T$$ .

What is the average net torque on the wheel during this time interval?

Accepted Answer

$$\frac{I\omega_f^{ }}{T^{ }}$$

Answer

$$\frac{\omega_f}{T}$$

Answer

$$\frac{\omega_f^{ }}{T^2}$$

Answer

$$\frac{I\omega_f^2}{T^{ }}$$

Question 19

A 5-kilogram sphere is connected to a 10-kilogram sphere by a rigid rod of negligible mass, as shown above. The sphere-rod combination can be pivoted about an axis that is perpendicular to the plane of the page and that passes through one of the five lettered points. Through which point should the axis pass for the moment of inertia of the sphere-rod combination about this axis to be greatest?

Accepted Answer

E

Answer

A

Answer

B

Answer

C

Answer

D

AP Physics 1: Chapter 8: Rotational Equilibrium and Dynamics

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