Chapter 10 Practice Test

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1 Chapter 10 Practice Test 1. At t = 0, a wheel rotating about a fixed axis at a constant angular acceleration of 0.40 rad/s 2 has an angular velocity of 1.5 rad/s and an angular position of 2.3 rad. What is the angular position of the wheel at t = 2.0 s? a. 4.9 rad b. 4.7 rad c. 4.5 rad d. 4.3 rad e. 4.1 rad 2. The turntable of a record player has an angular velocity of 8.0 rad/s when it is turned off. The turntable comes to rest 2.5 s after being turned off. Through how many radians does the turntable rotate after being turned off? Assume constant angular acceleration. a. 12 rad b. 8.0 rad c. 10 rad d. 16 rad e. 6.8 rad 3. A wheel starts from rest and rotates with a constant angular acceleration about a fixed axis. It completes the first revolution 6.0 s after it started. How long after it started will the wheel complete the second revolution? a. 9.9 s b. 7.8 s c. 8.5 s d. 9.2 s e. 6.4 s 4. A wheel rotates about a fixed axis with a constant angular acceleration of 4.0 rad/s 2. The diameter of the wheel is 40 cm. What is the linear speed of a point on the rim of this wheel at an instant when that point has a total linear acceleration with a magnitude of 1.2 m/s 2? a. 39 cm/s b. 42 cm/s c. 45 cm/s d. 35 cm/s e. 53 cm/s

2 5. A mass (M 1 = 5.0 kg) is connected by a light cord to a mass (M 2 = 4.0 kg) which slides on a smooth surface, as shown in the figure. The pulley (radius = 0.20 m) rotates about a frictionless axle. The acceleration of M 2 is 3.5 m/s 2. What is the moment of inertia of the pulley? a kg m 2 b kg m 2 c kg m 2 d kg m 2 e kg m 2 6. A wheel (radius = 0.25 m) is mounted on a frictionless, horizontal axis. The moment of inertia of the wheel about the axis is kg m 2. A light cord wrapped around the wheel supports a kg object as shown in the figure. The object is released from rest. What is the magnitude of the acceleration of the 0.50-kg object? a. 3.0 m/s 2 b. 3.4 m/s 2 c. 4.3 m/s 2 d. 3.8 m/s 2 e. 2.7 m/s 2

3 7. Two particles (m 1 = 0.20 kg, m 2 = 0.30 kg) are positioned at the ends of a 2.0-m long rod of negligible mass. What is the moment of inertia of this rigid body about an axis perpendicular to the rod and through the center of mass? a kg m 2 b kg m 2 c. 1.2 kg m 2 d kg m 2 e kg m 2 8. Particles (mass of each = 0.40 kg) are placed at the 60-cm and 100-cm marks of a meter stick of negligible mass. This rigid body is free to rotate about a frictionless pivot at the 0-cm end. The body is released from rest in the horizontal position. What is the magnitude of the initial linear acceleration of the end of the body opposite the pivot? a. 15 m/s 2 b. 9.8 m/s 2 c. 5.8 m/s 2 d. 12 m/s 2 e. 4.7 m/s 2 9. A uniform rod of length (L = 2.0 m) and mass (M = 1.5 kg) is pivoted about a horizontal frictionless pin through one end. The rod is released from rest at an angle of 30 below the horizontal. What is the angular speed of the rod when it passes through the vertical position? (The moment of inertia of the rod about the pin is 2.0 kg m 2.) a. 3.5 rad/s b. 2.7 rad/s c. 3.1 rad/s d. 2.3 rad/s e. 1.6 rad/s 10. The rigid body shown is rotated about an axis perpendicular to the paper and through the point P. If M = 0.40 kg, a = 30 cm, and b = 50 cm, how much work is required to take the body from rest to an angular speed of 5.0 rad/s? Neglect the mass of the connecting rods and treat the masses as particles. a. 2.9 J b. 2.6 J c. 3.1 J d. 3.4 J e. 1.6 J

4 11. Two people are on a ride where the inside cars rotate at constant angular velocity three times the constant angular velocity of the outer cars. If the two cars are in line at t = 0, and moving at 3ω and ω respectively, at what time will they next pass each other? a. t = 0. b. t = pi/2w. c. t = pi/w. d. t = 2pi/w. e. t = 3pi/w. 12. A uniform sphere of radius R and mass M rotates freely about a horizontal axis that is tangent to an equatorial plane of the sphere, as shown below. The moment of inertia of the sphere about this axis is a. 2/5 MR 2. b. 2/3 MR 2. c. 5/7 MR 2. d. 7/5 MR 2. e. 3/2 MR A small sphere attached to a light rigid rod rotates about an axis perpendicular to and fixed to the other end of the rod. Relative to the positive direction of the axis of rotation, the angular positions of the sphere are negative, its angular velocity is negative, and its angular acceleration is negative. The sphere is a. rotating clockwise and slowing down. b. rotating counterclockwise and slowing down. c. rotating clockwise and speeding up. d. rotating counterclockwise and speeding up. e. first rotating counterclockwise and then clockwise.

5 14. The graph below shows a plot of angular acceleration in rad/s 2 versus time from t = 0 s to t = 8 s. The change in angular velocity, Δω, during this 8-second period is a. 18 rad/s, CW. b. 18 rad/s, CCW. c. 23 rad/s, CW. d. 23 rad/s, CCW. e. 31 rad/s, CW. 15. When a wheel is rolling without slipping, the magnitude of its velocity relative to the ground is greatest at a. the point in contact with the ground. b. the point at the center of the wheel. c. the point at the top of the wheel opposite to the point in contact with the ground. d. the point farthest forward from the center of mass of the wheel. e. the point farthest behind the center of mass of the wheel.

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