AP Physics C: Mechanics Unit 5 Practice Test & Exam | 18 Questions

Questions 1-3 refer to the following information.

1. What is the magnitude of the average angular acceleration of the disk during the interval from $t=0$ s to $t=4$ s?

(A)$0.5 \text{ rad/s}^2$(B)$2.0 \text{ rad/s}^2$(C)$8.0 \text{ rad/s}^2$(D)$16.0 \text{ rad/s}^2$

2. What is the total angular displacement of the disk during the interval from $t=0$ s to $t=4$ s?

(A)$2 \text{ rad}$(B)$8 \text{ rad}$(C)$16 \text{ rad}$(D)$32 \text{ rad}$

3. A small dot is painted on the edge of the disk at a radius of $0.5$ m from the center. What is the magnitude of the tangential component of the linear acceleration of the dot at $t=2$ s?

(A)$0.5 \text{ m/s}^2$(B)$1.0 \text{ m/s}^2$(C)$2.0 \text{ m/s}^2$(D)$4.0 \text{ m/s}^2$

Questions 4-5 refer to the following information.

4. What is the magnitude of the net torque about the pivot P? (Define counter-clockwise as positive.)

(A)$F L (\frac{1}{2} + \frac{\sqrt{3}}{2})$(B)$-F L (\frac{1}{2} + \frac{1}{2})$(C)$-F L (\frac{1}{2} + \sin 30^\circ)$(D)$F L (\cos 30^\circ)$

5. Which of the following statements correctly describes the torques produced by the forces about pivot P?

(A)$\vec{F}1$ and $\vec{F}2$ produce torques in the same direction, while $\vec{F}_3$ produces zero torque.(B)$\vec{F}1$ and $\vec{F}2$ produce torques in opposite directions, while $\vec{F}_3$ produces a non-zero torque.(C)All three forces produce clockwise torques.(D)$\vec{F}2$ and $\vec{F}3$ produce torques in opposite directions.

6. A thin, uniform rod of length $L$ and mass $M$ has a rotational inertia of $\frac{1}{12}ML^2$ about an axis through its center of mass. What is the rotational inertia of the rod about an axis located at a distance of $L/4$ from one end?

(A)$\frac{1}{12}ML^2$(B)$\frac{1}{6}ML^2$(C)$\frac{7}{48}ML^2$(D)$\frac{13}{48}ML^2$

7. The rotational inertia of a solid object about an axis is to be calculated using the integral $I = \int r^2 dm$. For a uniform solid cylinder of radius $R$, height $H$, and total mass $M$, rotating about its central axis, the mass element $dm$ can be expressed in terms of the radial distance $r$ and a differential element $dr$ as $dm = \rho (2\pi r H) dr$. Which of the following integrals correctly represents the rotational inertia of the cylinder?

(A)$\int_0^R r^2 (\rho 2\pi r H) dr$(B)$\int_0^R r (\rho 2\pi r H) dr$(C)$\int_0^H r^2 (\rho \pi R^2) dr$(D)$\int_0^M r^2 dm$

8. A solid sphere and a hollow sphere, each with the same mass $M$ and radius $R$, are released from rest at the top of an inclined plane. Both roll without slipping. Which of the following statements is true about the objects when they reach the bottom of the incline?

(A)The solid sphere arrives first because it has a smaller rotational inertia.(B)The hollow sphere arrives first because it has a larger rotational inertia.(C)They arrive at the same time because they have the same mass and radius.(D)They arrive at the same time because the work done by gravity is the same for both.

9. A horizontal meter stick of negligible mass is in static equilibrium, as shown. It is pivoted at the 50 cm mark. A 2 kg mass hangs at the 20 cm mark. Where must a 4 kg mass be hung to balance the stick?

(A)At the 15 cm mark(B)At the 35 cm mark(C)At the 65 cm mark(D)At the 80 cm mark

10. A solid disk with mass $M$, radius $R$, and rotational inertia $I = \frac{1}{2}MR^2$ is free to rotate about a frictionless axle. A string is wrapped around the disk, and a block of mass $m$ is attached to the end of the string. The block is released from rest. What is the magnitude of the linear acceleration of the block?

(A)$g$(B)$\frac{mg}{m+M}$(C)$\frac{mg}{m + M/2}$(D)$\frac{mg}{M}$

11. The angular position of a flywheel is given by the function $\theta(t) = 2.0t^3 - 6.0t^2$. At what time $t > 0$ does the flywheel momentarily have zero angular velocity?

(A)$t = 1.0 \text{ s}$(B)$t = 2.0 \text{ s}$(C)$t = 3.0 \text{ s}$(D)$t = 6.0 \text{ s}$

12. A student applies a constant torque to a bicycle wheel, causing it to accelerate from rest. The student then applies the same constant torque to a second wheel that has the same mass but a larger rotational inertia. How does the angular acceleration of the second wheel compare to the first?

(A)It is greater, because the mass is the same.(B)It is smaller, because the rotational inertia is larger.(C)It is the same, because the applied torque is the same.(D)It is the same, because the mass is the same.

13. A merry-go-round rotates with a constant angular velocity $\omega$. Person A stands on the edge at radius $R$, and Person B stands halfway to the center at radius $R/2$. Which of the following correctly compares the kinematic quantities of the two people?

(A)They have the same angular velocity and the same tangential speed.(B)They have the same angular velocity, but Person A has twice the tangential speed of Person B.(C)Person A has twice the angular velocity and twice the tangential speed of Person B.(D)They have the same tangential speed, but Person A has half the angular velocity of Person B.

14. A force $\vec{F} = (3\hat{i} + 4\hat{j})$ N is applied to an object at a position $\vec{r} = (2\hat{i})$ m relative to a pivot. What is the resulting torque $\vec{\tau}$ about the pivot?

(A)$6\hat{k}$ N·m(B)$8\hat{k}$ N·m(C)$-8\hat{k}$ N·m(D)$12\hat{k}$ N·m

15. An object is subject to two forces of equal magnitude and opposite direction that are applied at two different points. This pair of forces is called a couple. Which of the following statements about the effect of a couple on the object is correct?

(A)The net force and the net torque are both zero.(B)The net force is zero, but the net torque may be non-zero.(C)The net torque is zero, but the net force may be non-zero.(D)The net force and the net torque are both non-zero.

Questions 16-18 refer to the following information.

16. What is the magnitude of the initial angular acceleration of the rod at the moment it is released?

(A)$\frac{g}{L}$(B)$\frac{2g}{3L}$(C)$\frac{3g}{2L}$(D)$\frac{g}{2L}$

17. As the rod swings from the horizontal position to the vertical position, how does the magnitude of its angular acceleration $\alpha$ change?

(A)It increases.(B)It decreases.(C)It remains constant.(D)It increases then decreases.

18. Which of the following principles is most appropriate for finding the angular speed of the rod when it reaches the vertical position? Section II: Free-Response Directions:Show all your work. You will be graded on the correctness of your methods as well as on the accuracy of your final answers. FRQ 1[Skills: 2.C, 4.C, 4.D, 5.B | Topics: 5.3, 5.6] Students are asked to determine the rotational inertia $I$ of a bicycle wheel of mass $M$ and radius $R$. The wheel is mounted on a low-friction axle. A light string is wrapped around the outer rim of the wheel, and a small mass $m$ is attached to the free end of the string. The mass is released from rest and allowed to fall a distance $h$, causing the wheel to rotate. FRQ 2[Skills: 1.A, 6.C, 7.A | Topics: 5.2, 5.6] A solid, uniform cylinder of mass $M$ and radius $R$ is released from rest at the top of an inclined plane of height $H$. The plane makes an angle $\theta$ with the horizontal. The cylinder rolls down the incline without slipping. The rotational inertia of a solid cylinder about its central axis is $I = \frac{1}{2}MR^2$. FRQ 3[Skills: 6.C, 7.D | Topics: 5.1, 5.3, 5.6] A thin, uniform rod of length $L=2.0$ m and mass $M=5.0$ kg is pivoted at its center. The rod is initially at rest in a horizontal position. Two forces are applied to the rod as shown. Force $\vec{F}1$ has a magnitude of 30 N and is applied perpendicularly at the left end. Force $\vec{F}2$ has a magnitude of 20 N and is applied at an angle of $30^\circ$ to the rod at the right end. The rotational inertia of a rod about its center is $I = \frac{1}{12}ML^2$. FRQ 4[Skills: 6.B, 6.C | Topics: 5.1, 5.4] A thin, flat, uniform plate of mass $M$ is in the shape of a rectangle with width $W$ and length $L$. It is rotated about an axis that is perpendicular to the plate and passes through one corner.

(A)The rotational inertia of a rectangular plate about an axis through its center of mass and perpendicular to the plate is $I_{cm} = \frac{1}{12}M(L^2 + W^2)$. Derive an expression for the rotational inertia $I$ of the plate about an axis perpendicular to the plate and passing through one corner. Express your answer in terms of $M, L,$ and $W$.(B)Now consider a specific case where the plate is a square with side length $L$ (so $W=L$). A torque given by the function $\tau(t) = \beta t$ is applied to the square plate, where $\beta$ is a positive constant. The plate starts from rest at $t=0$. Derive an expression for the angular velocity $\omega$ of the plate as a function of time $t$. Express your answer in terms of $M, L, \beta,$ and $t$.(C)The forces are applied for 3.0 s. Calculate the angular velocity of the rod at $t=3.0$ s.(D)A hollow hoop of the same mass $M$ and radius $R$ is now rolled down the same incline. The rotational inertia of the hoop is $I_{hoop} = MR^2$. Will the final speed of the hoop be greater than, less than, or equal to the final speed of the solid cylinder? Justify your answer without deriving the speed of the hoop.

AP Physics C: Mechanics Unit 5: Torque and Rotational Dynamics Practice Exam

Exam Details

A. Multiple-Choice Questions (18 Questions)

AP Physics C: Mechanics Unit 5: Torque and Rotational Dynamics Practice Exam

Exam Details

A. Multiple-Choice Questions (18 Questions)