AP Physics C: Mechanics ⚙️
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Answers and Review for Multiple Choice Practice on Systems of Rotation
Image courtesy of Pixabay
⛔STOP⛔ Before you look at the answers make sure you gave this practice quiz a try so you can assess your understanding of the concepts covered in Unit 5. Click here for the AP Physics C: Mechanics Multiple Choice Questions. Facts about the test: The AP Physics C: Mechanics exam has 35 multiple choice questions and you will be given 45 minutes to complete the section. That means it should take you around 15 minutes to complete 12 questions.
The following questions were not written by College Board and, although they cover information outlined in the AP Physics C: Mechanics Course and Exam Description, the formatting on the exam may be different.
1. An elevator travels downward with a linear speed of 1.2 m/s. The motion is controlled by an elevator cable attached to a pulley with a radius of 0.4m. What is the angular velocity of the pulley?
A. 3.0 rad/s
B. 4.0 rad/s
C. 6.0 rad/s
D. 12.0 rad/s
Answer: We know the linear speed of the rope, because it is the same as the elevator. Use v = r*omega and solve for omega to find the angular velocity. The radius is 0.4 meters.
📄Study AP Physics C: Mechanics, Unit 5.2: Rotational Kinematics
2. As shown in the image, two wheels are attached to each other and are free to rotate about a frictionless axis through their centers. Three forces are exerted tangent to the edge of the wheel. What is the magnitude of the net torque exerted on the system?
A. 10 Nm
B. 20 Nm
C. 25 Nm
D. 50 Nm
Answer: Choose one direction to be positive. Multiple the force times the lever arm for each of the three forces to find the torque applied, making sure to subtract any going in the negative direction. Then, add up the individual torques to find the net torque.
📄Study AP Physics C: Mechanics, Unit 5.3: Rotational Dynamics and Energy
3. A 3kg ball attached to a 2m long rope swings in a horizontal circle with a speed of 1.5 m/s. When the ball's acceleration is directed north, the ball's translational velocity vector points west. What is the magnitude and direction of the angular velocity vector?
A. 0.75 rad/s clockwise
B. 0.75 rad/s counterclockwise
C. 1.3 rad/s clockwise
D. 1.3 rad/s counterclockwise
Answer: To find the magnitude of the angular velocity vector, use v = omega*r and solve for omega. To find the direction of the vector, remember that the acceleration vector must point towards the center of the circle, and the velocity vector must point tangent to the circle in the direction of the motion. If you draw it out, you will see that the ball is at the bottom of the circle at this moment, and the velocity vector shows that the ball is moving clockwise.
📄Study AP Physics C: Mechanics, Unit 5.2: Rotational Kinematics
4. A car wheel (r = 0.8m) takes 150 revolutions to accelerate from rest to a linear velocity of 16 m/s. What is the angular acceleration of the wheel?
A. 0.2 rad/s/s
B. 2.0 rad/s/s
C. 20 rad/s/s
D. 200 rad/s/s
Answer: Use the relationship between linear and angular velocity, as well as the rotational kinematics equations to solve this problem. Remember that 1 revolution is equal to 2*pi radians!
📄Study AP Physics C: Mechanics, Unit 5.2: Rotational Kinematics
5. A 55kg person sits on a seesaw at a distance of 3 meters from the axis of rotation. A second person (m = 65kg) sits across from them. At what distance from the axis of rotation must the second person sit in order to be in static equilibrium?
A. 1.5 meters
B. 2.5 meters
C. 3 meters
D. 10 meters
Answer: In static equilibrium, the net torque is zero. Find the torque of the first person on the seesaw to equal 1650 Nm. Set that equal to the torque of the second person, and solve for the lever arm.
📄Study AP Physics C: Mechanics, Unit 5.1: Torque and Rotational Statics
6. An object with uniform mass density is rotated about a variety of axes shown in the image. Rotating around which of the axes will create the largest rotational inertia of the object?
A. A
B. B
C. C
D. D
Answer: Rotational inertia increases as the object's mass moves further away from the axis of rotation. Rotating the object around point D creates the furthest distance between the mass of the object and the axis of rotation.
📄Study AP Physics C: Mechanics, Unit 5.1: Torque and Rotational Statics
7. Two students sit on opposite ends of a massless see saw as shown in the image. What is the magnitude of the angular acceleration of the seesaw?
A. 2.9 rad/s
B. 4.0 rad/s
C. 5.7 rad/s
D. 8.0 rad/s
Answer: First, calculate the net torque on the system by each student. Then, use the rotational inertia equation to find the rotational inertia of the two students (treating them as point particles). Finally, use Newton's 2nd law for rotation to solve for angular acceleration.
📄Study AP Physics C: Mechanics, Unit 5.1: Torque and Rotational Statics
8. A solid sphere is rotated about its center, which has a rotational inertia of 2/5MR^2. What is the rotational inertia of the sphere if it is instead rotated around a point tangent to the edge of the sphere, a distance of R away?
A. MR^2
B. 4/25MR^2
C. 2/5MR
D. 7/5MR^2
Answer: Use the parallel axis theorem to answer this question. The distance between the center of the sphere and the axis of rotation is R. Add the initial rotational inertia and mR^2 to get 7/5MR^2.
📄Study AP Physics C: Mechanics, Unit 5.1: Torque and Rotational Statics
9. What is the rotational inertia of the two-mass system pictured in the image?
A. mR^2
B. 2mR^2
C. 4mR^2
D. 6mR^2
Answer: Use the rotational inertia equation to solve this problem. Find the rotational inertia of each mass by writing an expression using mr^2 for each, and then add them together.
📄Study AP Physics C: Mechanics, Unit 5.1: Torque and Rotational Statics
10. A ball starts from rest and rolls without slipping down a ramp with an initial height of 3 meters. Which of the following statements about the energy of the ball are true?
A. The total energy of the ball at the bottom of the ramp includes linear kinetic energy only.
B. The total energy of the ball at the bottom of the ramp includes rotational kinetic energy only.
C. The total energy of the ball at the bottom of the ramp includes both rotational and linear kinetic energy components.
D. The total energy of the ball at the bottom of the ramp includes rotational kinetic energy, linear kinetic energy, and gravitational potential energy.
Answer: At the bottom of the ramp, all of the initial gravitational potential energy has been transferred to kinetic energy, since the height of the ball is zero. Since the ball is rolling without slipping, both rotational and linear kinetic energy must be taken into account.
📄Study AP Physics C: Mechanics, Unit 5.3: Rotational Dynamics and Energy
11. A bowling ball starts from rest and rolls down an incline without slipping. Which of the following statements are true?
A. The initial potential energy of the ball is evenly divided into rotational and translational kinetic energy at the bottom of the incline.
B. There is only rotational kinetic energy at the bottom of the incline.
C. The amount of the rotational kinetic energy gained depends on the rotational inertia of the ball.
D. The amount of rotational kinetic energy the ball is determined solely based on the initial height of the incline.
Answer: Rotational kinetic energy depends on the rotational inertia of the ball and the angular velocity of the ball. It is not determined by the height of the incline. Translational kinetic energy exists throughout, and it is not necessarily evenly split with rotational kinetic energy.
📄Study AP Physics C: Mechanics, Unit 5.2: Rotational Kinematics
12. A hoop starts at rest on the top of a 1 meter tall incline. It rolls without slipping to the bottom of the incline. Which of the following is a correct expression for the angular velocity of the hoop at the bottom of the incline? Use I = mr^2.
A. g / r
B. g / r^2
C. 2g / r^2
D. sqrt(g) / r
Answer: Set the potential energy at the top of the ramp equal to the rotational + translational kinetic energy equations. Substitute 1m in for the change in height, mr^2 for I, and r*omega for v. Simplify. Remember that the masses cancel!
📄Study AP Physics C: Mechanics, Unit 5.2: Rotational Kinematics
13. A 2000kg carousel with a radius of 8 meters spins at a brisk 6m/s. What is the angular momentum of the carousel? Use the rotational inertia formula for a disk (I = 1/2mr^2)
A. 12000 kg*m^2/s
B. 24000 kg*m^2/s
C. 48000 kg*m^2/s
D. 64000 kg*m^2/s
Answer: Remember that angular momentum L = I*omega. Find omega using the translational velocity and the radius. Then, by using the angular velocity and the rotational inertia equation given, plug it all into the equation for angular momentum and solve.
📄Study AP Physics C: Mechanics, Unit 5.4: Angular Momentum and Its Conservation
14. A wheel spins clockwise. Which of the following correct describes the direction of the angular momentum vector of the wheel?
A. The vector is perpendicular to the wheel and pointing out of the computer screen.
B. The vector is perpendicular to the wheel and pointing into the computer screen.
C. The vector is parallel to the wheel and pointing left
D. The vector is parallel to the wheel and pointing right
Answer: Use the right hand rule! If you use your right hand and spin your fingers in the direction of the wheel's rotation, you will see that your thumb points into the computer screen.
📄Study AP Physics C: Mechanics, Unit 5.4: Angular Momentum and Its Conservation
15. A figure skater starts spinning on one skate with his arms spread out. He then keeps spinning and pulls his arms closer to his body. Which of the following statements are true?
A. Both the skater's angular momentum and rotational kinetic energy remain constant.
B. The skater's angular momentum remains constant, and his rotational kinetic energy decreases.
C. The skater's angular momentum increases, and his rotational kinetic energy remains constant.
D. The skater's angular momentum remains constant, and his rotational kinetic energy increases.
Answer: Since there are no external torques, the skater's angular momentum must remain constant. However, as he brings his arms in, he decreases his rotational inertia. In order to keep angular momentum constant, his angular velocity must increase. Rotational kinetic energy is directly proportional to the angular velocity squared, so it must increase, even though his rotational inertia decreases.
📄Study AP Physics C: Mechanics, Unit 5.4: Angular Momentum and Its Conservation
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