AP Physics 1: Algebra-Based Unit 5 Practice Test & Exam | 18 Questions

Refer to the figure below.

1. **1. [Skill: 2.A | Topic: 5.1]** A student records the angular position $θ$ (in radians) of a rigid object rotating about a fixed axis. The resulting $θ$ vs. $t$ graph is piecewise linear. [Image Cue]: Line graph, "Angular Position vs Time", horizontal axis: time $t$ (s) from 0 to 5, vertical axis: angular position $θ$ (rad). Key plotted points connected by straight lines: (0 s, 0 rad) to (2 s, 4 rad) to (5 s, 1 rad). What is the average angular velocity of the object from $t=2\ \text{s}$ to $t=5\ \text{s}$ ?

(A)$+1.0\ \text{rad/s}$(B)$-1.0\ \text{rad/s}$(C)$-3.0\ \text{rad/s}$(D)$-0.33\ \text{rad/s}$

Refer to the figure below.

2. **2. [Skill: 2.A | Topic: 5.1]** A rotating platform’s angular velocity is measured as a function of time. The graph of angular velocity $ω$ vs. time $t$ is a straight line. [Image Cue]: Line graph, "Angular Velocity vs Time", horizontal axis: time $t$ (s) from 0 to 4, vertical axis: angular velocity $ω$ (rad/s) from -6 to +6. A straight line increasing from point (0 s, -6 rad/s) to point (4 s, +6 rad/s), crossing ω = 0 at t = 2 s. Which statement is correct about the platform during the interval $0\le t\le 4\ \text{s}$?

(A)The average angular acceleration is $+3\ \text{rad/s}^2$, and the platform reverses its direction of rotation.(B)The average angular acceleration is $+3\ \text{rad/s}^2$, and the platform does not reverse its direction of rotation.(C)The average angular acceleration is $-3\ \text{rad/s}^2$, and the platform reverses its direction of rotation.(D)The average angular acceleration is $-3\ \text{rad/s}^2$, and the platform does not reverse its direction of rotation.

3. **3. [Skill: 5.A | Topic: 5.1]** A wheel starts from rest and speeds up with constant angular acceleration. After $10\ \text{s}$, its angular speed is $300\ \text{rev/min}$. What is the wheel’s angular displacement during the 10 s interval?

(A)$5\pi\ \text{rad}$(B)$25\pi\ \text{rad}$(C)$50\pi\ \text{rad}$(D)$100\pi\ \text{rad}$

4. [Skill: 2.A | Topic: 5.2] A rigid disk rotates about a fixed axis. Point P is located 0.20 m from the axis. During a time interval, the disk rotates through an angular displacement of 135°. What is the linear distance (arc length) traveled by point P during this interval?

(A)0.47 m(B)0.54 m(C)0.67 m(D)27 m

Refer to the figure below.

5. [Skill: 5.B | Topic: 5.2] A student uses a motion sensor system to determine the angular speed $\omega$ of a rotating platform as a function of time. Two small stickers, A and B, are placed on the platform at different distances from the axis: $r_A=0.10\ \text{m}$ and $r_B=0.30\ \text{m}$. [Image Cue]: Graph, "Angular speed vs. time", axes labeled $t$ (s) on horizontal and $\omega$ (rad/s) on vertical; a horizontal line at $\omega=6\ \text{rad/s}$ from $t=0$ to $t=4\ \text{s}$. At $t=2\ \text{s}$, what are the tangential speeds of stickers A and B?

(A)$v_A=0.6\ \text{m/s}$ and $v_B=1.8\ \text{m/s}$(B)$v_A=1.8\ \text{m/s}$ and $v_B=0.6\ \text{m/s}$(C)$v_A=6\ \text{m/s}$ and $v_B=6\ \text{m/s}$(D)$v_A=0.20\ \text{m/s}$ and $v_B=0.60\ \text{m/s}$

6. [Skill: 6.C | Topic: 5.2] A rigid wheel spins about a fixed axis. Two points on the wheel are marked: point C at radius $r_C=0.20\ \text{m}$ and point D at radius $r_D=0.50\ \text{m}$. At some instant, measurements show the tangential accelerations are $a_{t,C}=0.80\ \text{m/s}^2$ and $a_{t,D}=2.0\ \text{m/s}^2$. Which claim is best supported by these measurements?

(A)The wheel is not rigid because points on a rigid object must have the same tangential acceleration.(B)The wheel’s angular acceleration is $\alpha=4.0\ \text{rad/s}^2$ and is consistent with rigid rotation.(C)The wheel’s angular acceleration is $\alpha=1.6\ \text{rad/s}^2$ because $\alpha=a_t r$.(D)Points C and D must have different angular accelerations because they have different tangential accelerations.

7. [Skill: 2.B | Topic: 5.3] A student applies a single force to a rigid bar that can rotate about a fixed pivot. For each trial, the student records the force magnitude $F$, the distance $r$ from the pivot to the point of application, and the angle $\theta$ between the position vector $\vec{r}$ and the force vector $\vec{F}$. Trial 1: $F=20\ \text{N}$, $r=0.40\ \text{m}$, $\theta=90^\circ$ Trial 2: $F=30\ \text{N}$, $r=0.25\ \text{m}$, $\theta=60^\circ$ Trial 3: $F=15\ \text{N}$, $r=0.60\ \text{m}$, $\theta=30^\circ$ Trial 4: $F=12\ \text{N}$, $r=0.70\ \text{m}$, $\theta=90^\circ$ Which trial produces the greatest torque magnitude about the pivot?

(A)Trial 1(B)Trial 2(C)Trial 3(D)Trial 4

Refer to the figure below.

8. [Skill: 1.B | Topic: 5.3] A uniform horizontal beam of length $2.0\ \text{m}$ is free to rotate about a pivot at its left end. Four forces act on the beam: - $\vec{F}_1 = 40\ \text{N}$ upward applied at the pivot - $\vec{F}_2 = 30\ \text{N}$ downward applied at a point $1.0\ \text{m}$ to the right of the pivot - $\vec{F}_3 = 20\ \text{N}$ applied horizontally to the right at the right end of the beam - $\vec{F}_4 = 10\ \text{N}$ upward applied at the right end of the beam Take counterclockwise torques to be positive. What is the net torque about the pivot due to these forces?

(A)+50 N·m (counterclockwise)(B)+20 N·m (counterclockwise)(C)-10 N·m (clockwise)(D)-30 N·m (clockwise)

Refer to the figure below.

9. [Skill: 2.B | Topic: 5.3] A student uses a wrench of length $0.25\ \text{m}$ to turn a bolt. The bolt acts as the pivot. A force of magnitude $80\ \text{N}$ is applied at the end of the wrench at an angle of $30^\circ$ above the wrench handle (the angle between $\vec{r}$ and $\vec{F}$ is $30^\circ$). What is the lever arm (the perpendicular distance from the pivot to the line of action of the force)?

(A)0.25 m(B)0.22 m(C)0.13 m(D)0.06 m

10. [Skill: 2.A | Topic: 5.4] A student models a system as three small masses attached to a lightweight rod. The rod lies along the x-axis, and the system rotates about a fixed axis perpendicular to the rod through x = 0. The masses are placed as follows: - Mass 1: m_1 = 0.20 kg at x = 0.30 m - Mass 2: m_2 = 0.10 kg at x = 0.60 m - Mass 3: m_3 = 0.30 kg at x = 0.90 m Which of the following is closest to the total rotational inertia of the system about the axis at x = 0 ?

(A)0.11 kg·m^2(B)0.30 kg·m^2(C)0.33 kg·m^2(D)0.54 kg·m^2

11. [Skill: 2.A | Topic: 5.4] A rigid object of total mass M = 2.0 kg rotates in a plane. About an axis through the object’s center of mass and perpendicular to the plane, its rotational inertia is measured to be $I_{cm}=0.17\,\text{kg·m}^2$. The object is then rotated about a new axis that is parallel to the center-of-mass axis but displaced by a perpendicular distance d = 0.40 m from the center of mass. What is the rotational inertia $I'$ about the new axis?

(A)0.25 kg·m^2(B)0.49 kg·m^2(C)0.81 kg·m^2(D)0.17 kg·m^2

12. [Skill: 1.B | Topic: 5.4] Two identical small masses are attached to the ends of a lightweight rod and rotate about a fixed axis perpendicular to the rod through its midpoint. Initially, each mass is a distance 0.50 m from the axis. The masses are then slid inward so that each is only 0.25 m from the axis, while their masses remain the same. By what factor does the total rotational inertia of the two-mass system change?

(A)It decreases by a factor of 4.(B)It decreases by a factor of 2.(C)It increases by a factor of 4.(D)It remains the same.

Refer to the figure below.

13. [Skill: 2A | Topic: 5.5] A student pushes on a rigid door that rotates about a vertical hinge. The student applies two horizontal forces at different distances from the hinge, as shown. [Image Cue]: Diagram, "Door with Two Applied Forces", top-down view. A vertical hinge line at the left edge of the door is the rotation axis. Force $\vec{F}_1$ is applied at a point 0.80 m from the hinge, perpendicular to the door (tangential). Force $\vec{F}_2$ is applied at a point 0.40 m from the hinge, also perpendicular to the door (tangential). Arrows indicate directions. The magnitudes are $F_1 = 10\ \text{N}$ and $F_2 = 20\ \text{N}$. $\vec{F}_1$ tends to rotate the door counterclockwise, and $\vec{F}_2$ tends to rotate the door clockwise. Which statement is correct about the door’s subsequent rotational motion (ignore friction)?

(A)The door’s angular velocity remains constant because the net torque about the hinge is zero.(B)The door’s angular velocity increases because the larger force ($20\ \text{N}$) produces a larger torque.(C)The door’s angular velocity remains constant only if the net force on the door is zero.(D)The door’s angular velocity must be zero because the torques cancel.

Refer to the figure below.

14. [Skill: 4A | Topic: 5.5] A uniform rigid rod lies on a nearly frictionless horizontal surface. Two students apply forces to the rod at the same time, as shown. [Image Cue]: Diagram, "Rod with Two Forces", top-down view. A horizontal rod of length 2.0 m is shown. At the left end, a force of 15 N is applied upward (north). At the right end, a force of 15 N is applied downward (south). Forces are parallel, equal in magnitude, opposite in direction, and applied at opposite ends. Which description best characterizes the rod’s motion immediately after the forces are applied?

(A)The rod is in both translational and rotational equilibrium because the forces are equal and opposite.(B)The rod is in translational equilibrium but not rotational equilibrium, so it begins rotating while its center of mass remains at rest.(C)The rod is in rotational equilibrium but not translational equilibrium, so it translates without rotating.(D)The rod is in neither translational nor rotational equilibrium, so it both translates and rotates.

Refer to the figure below.

15. [Skill: 1B | Topic: 5.5] A rigid wheel rotates about a fixed axle with negligible friction. The net external torque about the axle, $\tau_{\text{net}}$, is measured as a function of time and shown in the graph. [Image Cue]: Graph, "Net Torque vs. Time", x-axis: time t (s) from 0 to 6; y-axis: $\tau_{\text{net}}$ (N·m). From t = 0 to 2 s, $\tau_{\text{net}} = +4$ N·m (constant). From t = 2 to 4 s, $\tau_{\text{net}} = 0$. From t = 4 to 6 s, $\tau_{\text{net}} = -4$ N·m (constant). Which statement about the wheel’s angular velocity $\omega$ is most consistent with the graph?

(A)$\omega$ is constant from 0 to 2 s, increases from 2 to 4 s, and decreases from 4 to 6 s.(B)$\omega$ increases from 0 to 2 s, is constant from 2 to 4 s, and decreases from 4 to 6 s.(C)$\omega$ is constant for the entire 0 to 6 s interval because the positive and negative torques cancel overall.(D)$\omega$ must be zero from 2 to 4 s because the net torque is zero in that interval.

Refer to the figure below.

16. **1. [Skill: 4A | Topic: 5.6]** A student investigates how the angular acceleration of a rigid disk depends on the torque applied by a motor. The student measures the disk’s angular acceleration $\alpha$ for different applied torques $\tau_{app}$. The results are shown in the graph. [Image Cue]: Graph, "Angular acceleration vs. applied torque", horizontal axis $\tau_{app}$ (N·m) from 0 to 1.4, vertical axis $\alpha$ (rad/s^2) from -1 to 6. The data lie on a straight line passing through approximately $(0.20\ \text{N·m},\ 0\ \text{rad/s}^2)$ and $(1.20\ \text{N·m},\ 5.0\ \text{rad/s}^2)$. Assume the disk experiences a constant friction torque that opposes the direction of rotation. If the disk is rotating in the positive direction and the motor applies $\tau_{app}=0.15\ \text{N·m}$ in the positive direction, which statement best describes the disk’s angular velocity immediately after this torque is applied?

(A)It increases because $\tau_{app}$ is positive.(B)It remains constant because $\tau_{app}$ is less than 0.20 N·m.(C)It decreases because the net torque is negative.(D)It decreases because the rotational inertia must be decreasing.

Refer to the figure below.

17. **2. [Skill: 3A | Topic: 5.6]** A uniform rigid rod of length $L$ is mounted on a frictionless pivot at its left end. Two forces act on the rod in the plane of the page, as shown. [Image Cue]: Diagram, "Rod with forces", a horizontal rod of length $L$ pivoted at the left end. Force $\vec{F}_1$ of magnitude $F$ is applied downward at the right end (distance $L$ from pivot). Force $\vec{F}_2$ of magnitude $F$ is applied upward at the midpoint (distance $L/2$ from pivot). Indicate distances $L$ and $L/2$. Which statement best describes the rod’s initial angular acceleration about the pivot immediately after the forces are applied?

(A)The angular acceleration is zero because the forces have equal magnitude.(B)The rod has a nonzero angular acceleration clockwise because the net torque is clockwise.(C)The rod has a nonzero angular acceleration counterclockwise because the net torque is counterclockwise.(D)The angular acceleration cannot be determined without knowing the rod’s mass.

18. **3. [Skill: 3A | Topic: 5.6]** A block of mass $m=2.0\ \text{kg}$ hangs from a light string that is wrapped around a fixed pulley of radius $R=0.20\ \text{m}$. The pulley has rotational inertia $I=0.50\ \text{kg·m}^2$. The string does not slip on the pulley. The system is released from rest, and the block moves downward. Take $g=9.8\ \text{m/s}^2$. What is the magnitude of the pulley’s angular acceleration $\alpha$ just after release?

(A)$2.0\ \text{rad/s}^2$(B)$6.8\ \text{rad/s}^2$(C)$9.8\ \text{rad/s}^2$(D)$49\ \text{rad/s}^2$

AP Physics 1: Algebra-Based Unit 5: Torque and Rotational Dynamics Practice Exam

Exam Details

A. Multiple-Choice Questions (18 Questions)

AP Physics 1: Algebra-Based Unit 5: Torque and Rotational Dynamics Practice Exam

Exam Details

A. Multiple-Choice Questions (18 Questions)