1. A cylinder with rotational inertia /₁ = 2.0 kgm² rotates clockwise about a vertical axis through its center with angular speed w, = 5.0 rad/s. A second cylinder with rotational inertia 12 = 12 = 2.0 kgm2 rotates counter-clockwise about the same axis with angular speed w₂ = 8.0 rad/s. a) Assuming no external torques act on the system of cylinders, if the cylinders couple so they have the same rotational axis, what is the angular speed of the combination? Hint: Pick a direction for the angular momentum. Let counter-clockwise rotation correspond to a positive L and a clockwise rotation correspond to a negative L. rad/s W= b) What percentage of the kinetic energy is lost during the coupling?

1. A cylinder with rotational inertia /₁ = 2.0 kgm² rotates clockwise about a vertical axis through its center with angular speed w, = 5.0 rad/s. A second cylinder with rotational inertia 12 = 12 = 2.0 kgm2 rotates counter-clockwise about the same axis with angular speed w₂ = 8.0 rad/s. a) Assuming no external torques act on the system of cylinders, if the cylinders couple so they have the same rotational axis, what is the angular speed of the combination? Hint: Pick a direction for the angular momentum. Let counter-clockwise rotation correspond to a positive L and a clockwise rotation correspond to a negative L. rad/s W= b) What percentage of the kinetic energy is lost during the coupling?

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter10: Rotational Motion

Section: Chapter Questions

Problem 18P: Rigid rods of negligible mass lying along the y axis connect three particles (Fig. P10.18). The...

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A large grinding wheel in the shape of a solid cylinder of radius 0.330 m is free to rotate on a friction less, vertical axle. A constant tangential force of 250. N applied to its edge causes the wheel to have an angular acceleration of 0.940 rad/s2. (a) What is the moment of inertia of the wheel? (b) What is the mass of the wheel? (c) If the wheel starts from rest, what is its angular velocity after 5.00 s have elapsed, assuming the force is acting during that time?
A disk with moment of inertia I1 rotates about a frictionless, vertical axle with angular speed i. A second disk, this one having moment of inertia I2 and initially not rotating, drops onto the first disk (Fig. P10.50). Because of friction between the surfaces, the two eventually reach the same angular speed f. (a) Calculate f. (b) Calculate the ratio of the final to the initial rotational energy. Figure P10.50
Rigid rods of negligible mass lying along the y axis connect three particles (Fig. P10.18). The system rotates about the x axis with an angular speed of 2.00 rad/s. Find (a) the moment of inertia about the x axis, (b) the total rotational kinetic energy evaluated from 12I2, (c) the tangential speed of each particle, and (d) the total kinetic energy evaluated from 12mivi2. (e) Compare the answers for kinetic energy in parts (b) and (d). Figure P10.18
Rotational Inertia Problems 5 and 6 are paired. 5. N A system consists of four boxes modeled as particles connected by very lightweight, stiff rods (Fig. P13.5). The system rotates around the z axis, which points out of the page. Each particle has a mass of 5.00 kg. The distances from the z axis to each particle are r1 = 32.0 cm, r2 = 16.0 cm, r3 = 17.0 cm, and r4 = 34.0 cm. Find the rotational inertia of the system around the z axis. 6. N Use the information in Problem 5 to find the rotational inertia of the system around particle 1. FIGURE P13.5 Problems 5 and 6.
A constant net torque is applied to an object. Which one of the following will not be constant? (a) angular acceleration, (b) angular velocity, (c) moment of inertia, or (d) center of gravity.
If the system shown in Figure P8.37 is set in rotation about each of the axes mentioned in Problem 37, find the torque that will produce an angular acceleration of 1.50 rad/s2 in each case. Figure P8.37 Problems 37 and 38.
The combination of an applied force and a friction force produces a constant total torque of 36.0 N m on a wheel rotating about a fixed axis. The applied force acts for 6.00 s. During this time, the angular speed of the wheel increases from 0 to 10.0 rad/s. The applied force is then removed, and the wheel comes to rest in 60.0 s. Find (a) the moment of inertia of the wheel, (b) the magnitude of the torque due to friction, and (c) the total number of revolutions of the wheel during the entire interval of 66.0 s.
The angular speed of a wheel is given by (t) = 72.5 rad/s + (9.34 rad /s2) t. a. Is the wheels angular acceleration constant? Explain. b. Find an expression for the angular acceleration.
The uniform thin rod in Figure P8.47 has mass M = 3.50 kg and length L = 1.00 m and is free to rotate on a friction less pin. At the instant the rod is released from rest in the horizontal position, find the magnitude of (a) the rods angular acceleration, (b) the tangential acceleration of the rods center of mass, and (c) the tangential acceleration of the rods free end. Figure P8.47 Problems 47 and 86.