AP Physics 1: Algebra-Based Unit 6 Practice Test & Exam | 19 Questions

1. [Skill: 5B | Topic: 6.1] A student investigates the rotational kinetic energy of an object spinning about a fixed axis. The student records the angular speed and calculates the rotational kinetic energy for several trials. The results are shown. Trial 1: ω = 10 rad/s, K_rot = 2.0 J Trial 2: ω = 20 rad/s, K_rot = 8.0 J Trial 3: ω = 30 rad/s, K_rot = 18 J Assuming the object behaves as a rigid system, what is the best estimate of the object’s rotational inertia I about the axis of rotation?

(A)0.020 kg·m^2(B)0.040 kg·m^2(C)0.080 kg·m^2(D)0.20 kg·m^2

2. [Skill: 2A | Topic: 6.1] A rigid cart-wheel system of total mass 2.0 kg moves to the right on a frictionless horizontal track while the wheel rotates about its center of mass. At an instant, the center of mass of the system has speed 3.0 m/s, the wheel’s angular speed about its center is 6.0 rad/s, and the rotational inertia of the rotating part about its center is 0.50 kg·m^2. What is the total kinetic energy of the system at that instant?

(A)9.0 J(B)12 J(C)18 J(D)27 J

3. [Skill: 1A | Topic: 6.1] Two 0.40 kg point masses are attached to the ends of a light (negligible mass) rod of length 1.0 m. The rod rotates in a horizontal plane about an axis through its midpoint and perpendicular to the rod. The midpoint of the rod is fixed, so the center of mass of the two-mass system remains at rest. At a particular instant, the angular speed of the rod is 5.0 rad/s. What is the kinetic energy of the system at that instant?

(A)0 J, because the center of mass is at rest(B)1.25 J(C)2.5 J(D)10 J

4. **1. [Skill: 3.B | Topic: 6.2]** A student uses a wrench to tighten a bolt, applying a constant torque of magnitude 12 N·m to the bolt. While the student applies this torque, the bolt rotates through an angular displacement of 0.75 rad in the same direction as the torque. Which of the following best states the work done by the torque on the bolt and the corresponding change in the bolt’s rotational kinetic energy?

(A)The torque does +9.0 J of work, so the bolt’s rotational kinetic energy increases by 9.0 J.(B)The torque does +16 J of work, so the bolt’s rotational kinetic energy increases by 16 J.(C)The torque does −9.0 J of work, so the bolt’s rotational kinetic energy decreases by 9.0 J.(D)The torque does 0 J of work, so the bolt’s rotational kinetic energy does not change.

5. **2. [Skill: 3.B | Topic: 6.2]** A rigid disk rotates about a fixed axis. Two constant torques act on the disk during the same interval: a 4.0 N·m torque in the clockwise direction and a 1.5 N·m torque in the counterclockwise direction. During the interval, the disk rotates 2.0 rad clockwise. Take clockwise to be the positive direction. What is the net work done on the disk by the two torques during this interval?

(A)5.0 J(B)11 J(C)−5.0 J(D)−11 J

Refer to the figure below.

6. **3. [Skill: 4.A | Topic: 6.2]** The graph shows the torque $\tau$ exerted on a rigid object as a function of its angular position $\theta$ as it rotates about a fixed axis. What is the total work done on the object by the torque as the object rotates from $\theta=0$ rad to $\theta=5$ rad?

(A)9 J(B)15 J(C)18 J(D)−15 J

7. **1. [Skill: 2.A | Topic: 6.3]** A motor spins a rigid wheel about a fixed axis. The wheel’s rotational inertia about the axis is $I = 0.40\ \text{kg}\cdot\text{m}^2$. A sensor records that the wheel’s angular speed increases linearly from $\omega = 0\ \text{rad/s}$ at $t=0$ to $\omega = 12\ \text{rad/s}$ at $t=3.0\ \text{s}$. What is the magnitude of the wheel’s angular momentum about the axis at $t=2.0\ \text{s}$?

(A)1.1 kg·m^2/s(B)3.2 kg·m^2/s(C)4.8 kg·m^2/s(D)6.4 kg·m^2/s

8. **2. [Skill: 2.A | Topic: 6.3]** A particle of mass $m = 0.20\ \text{kg}$ moves with speed $v = 15\ \text{m/s}$. At a particular instant, the particle is at a distance $r = 0.50\ \text{m}$ from a point $P$. The velocity vector makes an angle of $30^\circ$ with the position vector drawn from $P$ to the particle. What is the magnitude of the particle’s angular momentum about point $P$ at that instant?

(A)0.43 kg·m^2/s(B)0.75 kg·m^2/s(C)1.3 kg·m^2/s(D)2.3 kg·m^2/s

Refer to the figure below.

9. **3. [Skill: 5.B | Topic: 6.3]** A rigid wheel rotates about a fixed axis. At $t=0$, the wheel’s angular momentum about the axis is $L_0 = 1.5\ \text{kg}\cdot\text{m}^2/\text{s}$. A net external torque $\tau$ about the axis acts on the wheel with the time dependence shown. [Image Cue]: Graph, Net torque vs time, vertical axis $\tau$ (N·m) and horizontal axis t (s); piecewise constant: $\tau$=+2.0$\ \text{N·m}$ from t=0 to 1.0$\ \text{s}$, then $\tau$=-1.0$\ \text{N·m}$ from t=1.0$\ \text{s}$ to 3.0$\ \text{s}$. What is the wheel’s angular momentum at $t=3.0\ \text{s}$?

(A)0.50 kg·m^2/s(B)1.5 kg·m^2/s(C)3.5 kg·m^2/s(D)5.5 kg·m^2/s

10. [Skill: 3.A | Topic: 6.4] An ice skater is spinning about a vertical axis on nearly frictionless ice. Initially, the skater’s rotational inertia about the axis is $I_i = 4.0\ \text{kg}\cdot\text{m}^2$ and the skater’s angular speed is $\omega_i = 2.0\ \text{rad/s}$. The skater pulls their arms in, changing the rotational inertia to $I_f = 1.0\ \text{kg}\cdot\text{m}^2$. Assume the net external torque about the axis is negligible. Which of the following is the best value for the skater’s final angular speed $\omega_f$?

(A)0.50 rad/s(B)2.0 rad/s(C)8.0 rad/s(D)16 rad/s

11. [Skill: 2.B | Topic: 6.4] A rigid turntable rotates about a fixed vertical axis with constant angular speed $\omega = 1.5\ \text{rad/s}$. The turntable has rotational inertia $I_t = 0.80\ \text{kg}\cdot\text{m}^2$. Two small masses are attached and rotate with the turntable: $m_1 = 20\ \text{kg}$ at radius $r_1 = 0.50\ \text{m}$ and $m_2 = 20\ \text{kg}$ at radius $r_2 = 0.50\ \text{m}$. What is the total angular momentum of the rotating system (turntable + both masses) about the vertical axis?

(A)1.2 kg·m^2/s(B)12 kg·m^2/s(C)16.2 kg·m^2/s(D)24.3 kg·m^2/s

12. [Skill: 4.A | Topic: 6.4] A student stands on a low-friction turntable that can rotate about a vertical axis. The student holds a bicycle wheel whose axle is vertical. Initially, the student+turntable system is not rotating. The wheel is spinning with angular speed $\omega_w = 20\ \text{rad/s}$ and rotational inertia $I_w = 0.60\ \text{kg}\cdot\text{m}^2$ about its axle, so the wheel’s angular momentum is upward (along +vertical). The student quickly flips the wheel over 180° so that the wheel’s angular momentum is downward (along −vertical). The rotational inertia of the student+turntable about the vertical axis is $I_s = 4.0\ \text{kg}\cdot\text{m}^2$. Assume the net external torque about the vertical axis is negligible. Which option correctly identifies a system for which angular momentum is conserved about the vertical axis during the flip AND gives the correct final angular speed of the student+turntable?

(A)System: wheel only; conserved, so the student+turntable remains at 0 rad/s.(B)System: student+turntable only; conserved, so the student+turntable remains at 0 rad/s.(C)System: wheel + student + turntable; conserved, and the student+turntable ends at 6 rad/s.(D)System: wheel + student + turntable; conserved, and the student+turntable ends at 3 rad/s.

Refer to the figure below.

13. [Skill: SP 2.A | Topic: 6.5] Three rigid objects start from rest at the top of the same incline of vertical drop h. Each object rolls down without slipping. Object 1: thin hoop, $I = mR^2$ Object 2: solid cylinder, $I = \tfrac{1}{2}mR^2$ Object 3: solid sphere, $I = \tfrac{2}{5}mR^2$ All three have the same mass m and radius R. Which object has the greatest translational speed of its center of mass at the bottom of the incline? [Image Cue]: Diagram, "Three objects rolling down the same incline," showing a ramp with height h and three objects labeled hoop/cylinder/sphere released from rest at the same starting line and ending at the same bottom point.

(A)Object 1 (thin hoop)(B)Object 2 (solid cylinder)(C)Object 3 (solid sphere)(D)All three have the same speed because they lose the same gravitational potential energy $mgh$

Refer to the figure below.

14. [Skill: SP 5.B | Topic: 6.5] A student tests whether a wheel rolls without slipping on a horizontal track by measuring the wheel’s angular speed $\omega$ and the speed v of the wheel’s center of mass. The student collects the following data: Trial 1: $\omega = 10\ \text{rad/s}$, $v = 0.50\ \text{m/s}$ Trial 2: $\omega = 20\ \text{rad/s}$, $v = 1.00\ \text{m/s}$ Trial 3: $\omega = 30\ \text{rad/s}$, $v = 1.55\ \text{m/s}$ Which conclusion is best supported by the data? [Image Cue]: Graph, "v vs. ω data for a rolling wheel," x-axis: $\omega$ (rad/s), y-axis: v (m/s), points at (10,0.50), (20,1.00), (30,1.55). Include a straight reference line through the origin with slope 0.050 m labeled "v = Rω" for R = 0.050 m.

(A)The wheel rolls without slipping in all trials, and the radius is $R = 0.050\ \text{m}$ exactly.(B)The wheel rolls without slipping for Trials 1 and 2 with $R \approx 0.050\ \text{m}$, but Trial 3 suggests slight slipping because v is slightly larger than $R\omega$.(C)The wheel is slipping in all trials because v is not constant.(D)The wheel cannot be rolling because rolling would require $v \propto \omega^2$, not $v \propto \omega$.

Refer to the figure below.

15. [Skill: SP 6.C | Topic: 6.5] A uniform solid cylinder rolls without slipping down a fixed incline. The cylinder starts from rest and speeds up as it descends. Consider the interaction between the cylinder and the incline at the contact point. Which statement about the work done by friction on the cylinder is correct for this ideal rolling-without-slipping situation? [Image Cue]: Free-body diagram, "Cylinder rolling down an incline," showing forces on the cylinder: weight $mg$ downward, normal force N perpendicular to the incline, and static friction $f_s$ directed up the incline (providing a torque about the center).

(A)Static friction does negative work on the cylinder, converting mechanical energy into thermal energy.(B)Static friction does positive work on the cylinder, increasing the cylinder’s total mechanical energy.(C)Static friction does zero work on the cylinder, even though it provides a torque that increases the cylinder’s rotational kinetic energy.(D)Static friction must be zero; otherwise rolling without slipping is impossible.

16. [Skill: 1.B | Topic: 6.6] A satellite of mass m moves in a stable circular orbit of radius r around a much more massive planet. The satellite’s engines are off, and the only significant interaction in the satellite–planet system is gravity. Which of the following sets of quantities is constant during the motion? Select the best answer.

(A)The satellite’s kinetic energy, the satellite–planet gravitational potential energy, the satellite’s angular momentum, and the system’s total mechanical energy(B)The satellite’s kinetic energy and the satellite’s angular momentum are constant, but the gravitational potential energy is not constant because the satellite’s velocity changes direction(C)The gravitational potential energy is constant, but the satellite’s kinetic energy is not constant because the satellite’s acceleration is nonzero(D)Only the system’s total mechanical energy is constant; the satellite’s kinetic energy, gravitational potential energy, and angular momentum all change continuously in circular motion

Refer to the figure below.

17. [Skill: 2.C | Topic: 6.6] A satellite of mass m is at a distance r from the center of a planet of mass M. The satellite is given an instantaneous speed v and then moves only under the influence of gravity. The graph shows the satellite–planet system’s total mechanical energy $E$ as a function of the satellite’s speed v at that same distance r. Which labeled point on the graph corresponds to the satellite having exactly the escape speed (the minimum speed that results in a trajectory with total mechanical energy equal to zero)?

(A)Point A(B)Point B(C)Point C(D)Point D

18. [Skill: 4.A | Topic: 6.6] A spacecraft of mass m orbits a planet of mass M, where $m \ll M$. A student models the planet as stationary and the spacecraft as moving in response to the planet’s gravitational force. Which of the following best justifies this modeling assumption?

(A)The spacecraft exerts no gravitational force on the planet because the planet is much more massive(B)The planet experiences the same magnitude gravitational force as the spacecraft, but its resulting acceleration is negligible because $m \ll M$(C)The gravitational forces on the planet from the spacecraft cancel over one orbit, so the planet’s net force is zero at every instant(D)Because the spacecraft is in circular motion, the planet must have zero velocity in all reference frames

AP Physics 1: Algebra-Based Unit 6: Energy and Momentum of Rotating Systems Practice Exam

Exam Details

A. Multiple-Choice Questions (18 Questions)

B. Short Answer Questions (1 Question)

AP Physics 1: Algebra-Based Unit 6: Energy and Momentum of Rotating Systems Practice Exam

Exam Details

A. Multiple-Choice Questions (18 Questions)

B. Short Answer Questions (1 Question)