Physics 111 Practice Problem Statements 10 Torque, Energy, Rolling SJ 8th Ed.: Chap 10.6 – 10.9 Contents 11-47, 11-49*, 11-55*, 11-56, 11-60*, 11-63, 11-66 12-5, 12-19, 12-21, Torque Newton’s Second Law for Rotation Energy Considerations in Rotational Motion Rolling Energy Methods Second Law Applications 8/8/2011

PROBLEM 11-47: The body in Fig PROBLEM 11-47: The body in Fig. 11-37 is pivoted at O, and two forces act on it as shown. (a) Find an expression for the net torque on the body about the pivot. (b) If r1 = 1.30 m, r2 = 2.15 m, F1 = 4.20 N, F2 = 4.90 N, q1 = 75.0°, and q2 = 60.0°, what is the net torque about the pivot? 8/8/2011

PROBLEM 11-49*: During the launch from a board, a diver's angular speed about her center of mass changes from zero to 6.20 rad/s in 220 ms. Her rotational inertia about her center of mass is 12.0 kg·m2. During the launch, what are the magnitudes of (a) her average angular acceleration and (b) the average external torque on her from the board? 8/8/2011

PROBLEM 11-55*: In Fig. 11-42, one block has mass M = 500 g, the other has mass m = 460 g, and the pulley, which is mounted in horizontal frictionless bearings, has a radius of 5.00 cm. When released from rest, the heavier block falls 75.0 cm in 5.00 s (without the cord slipping on the pulley). (a) What is the magnitude of the blocks' acceleration? What is the tension in the part of the cord that supports (b) the heavier block and (c) the lighter block? (d) What is the magnitude of the pulley's angular acceleration? (e) What is its rotational inertia? 8/8/2011

PROBLEM 11-56: A pulley, with a rotational inertia of 1 PROBLEM 11-56: A pulley, with a rotational inertia of 1.0 10-3 kg·m2 about its axle and a radius of 10 cm, is acted on by a force applied tangentially at its rim. The force magnitude varies in time as F = 0.50t + 0.30t2, with F in newtons and t in seconds. The pulley is initially at rest. At t = 3.0 s what are (a) its angular acceleration and (b) its angular speed? 8/8/2011

PROBLEM 11-60*: A 32.0 kg wheel, essentially a thin hoop with radius 1.20 m, is rotating at 280 rev/min. It must be brought to a stop in 15.0 s. (a) How much work must be done to stop it? (b) What is the required average power? 8/8/2011

PROBLEM 11-63: A meter stick is held vertically with one end on the floor and is then allowed to fall. Find the speed of the other end when it hits the floor, assuming that the end on the floor does not slip. (Hint: Consider the stick to be a thin rod and use the conservation of energy principle.) 8/8/2011

PROBLEM 11-66: A uniform spherical shell of mass M and radius R rotates about a vertical axis on frictionless bearings (Fig. 11-45). A massless cord passes around the equator of the shell, over a pulley of rotational I and radius r, and is attached to a small object of mass m. There is no friction on the pulley's axle; the cord does not slip on the pulley. What is the speed of the object after it falls a distance h from rest? Use energy considerations. 8/8/2011

Problem 12-5: A 1000 kg car has four 10 kg wheels Problem 12-5: A 1000 kg car has four 10 kg wheels. When the car is moving, what fraction of the total kinetic energy of the car is due to rotation of the wheels about their axles? Assume that the wheels have the same rotational inertia as uniform disks of the same mass and size. Why do you not need the radius of the wheels? 8/8/2011

Problem 12-19: What are the magnitude and direction of the torque about the origin on a particle located at coordinates (0, -4.0 m, 3.0 m) due to (a) force F1 with components F1x = 2.0 N and F1y = F1z = 0, and (b) force F2 with components F2x = 0, F2y = 2.0 N, and F2z = 4.0 N? 8/8/2011

Problem 12-21: Force F = (-8. 0 N)i + (6 Problem 12-21: Force F = (-8.0 N)i + (6.0 N)j acts on a particle with position vector r = (3.0 m)i + (4.0 m)j. What are (a) the torque on the particle about the origin and (b) the angle between the directions of r and F ? 8/8/2011