A hollow sphere of radius 0.230 m, with rotational inertia l = 0.0466 kg-m² about a line through its center of mass, rolls without slipping up a surface inclined at 31.7° to the horizontal. At a certain initial position, the sphere's total kinetic energy is 14.O J. (a) How much of this initial kinetic energy is rotational? (b) What is the speed of the center of mass of the sphere at the initial position? When the sphere has moved 0.940 m up the incline from its initial position, what are (c) its total kinetic energy and (d) the speed of its center of mass?

A hollow sphere of radius 0.230 m, with rotational inertia l = 0.0466 kg-m² about a line through its center of mass, rolls without slipping up a surface inclined at 31.7° to the horizontal. At a certain initial position, the sphere's total kinetic energy is 14.O J. (a) How much of this initial kinetic energy is rotational? (b) What is the speed of the center of mass of the sphere at the initial position? When the sphere has moved 0.940 m up the incline from its initial position, what are (c) its total kinetic energy and (d) the speed of its center of mass?

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...

See similar textbooks

Similar questions

Calculate the rotational kinetic energy of a 12-kg motorcycle wheel if its angular velocity is 120 rad/s and its inner radius is 0.280 m and outer radius 0.330 m.
A wheel starts from rest and in 12.65 s is rotating with an angular speed of 5.435 rad/s. a. Find the magnitude of theconstant angular acceleration of the wheel. b. Through whatangle does the wheel move in 6.325 s?
A solid cylinder of mass 2.0 kg and radius 20 cm is rotating counterclockwise around a vertical axis through its center at 600 rev/min. A second solid cylinder of the same mass and radius is rotating clockwise around the same vertical axis at 900 rev/min. If the cylinders couple so that they rotate about the same vertical axis, what is the angular velocity of the combination?
A constant torque is applied to a rigid body whose moment of inertia is 4.0kgm2 around the axis of rotation. If the wheel starts from rest and attains an angular velocity of 20.0 rad/s in 10.0 s, what is the applied torque?
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
A 12.0-kg solid sphere of radius 1.50 m is being rotated by applying a constant tangential force of 10.0 N at a perpendicular distance of 1.50 m from the rotation axis through the center of the sphere. If the sphere is initially at rest, how many revolutions must the sphere go through while this force is applied before it reaches an angular speed of 30.0 rad/s?
Two spheres, one hollow and one solid, are rotating with the same angular speed around an axis through their centers. Both spheres have the same mass and radius. Which sphere, if either, has the higher rotational kinetic energy? (a) The hollow I sphere, (b) The solid sphere, (c) They have the same kinetic energy.
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
A student rides his bicycle at a constant speed of 3.00 m/s along a straight, level road. If the bikes tires each have a radius of 0.350 m, (a) what is the tires angular speed? (See Section 7.3.) (b) What is the net torque on each tire? (See Section 8.5.)
A potters wheel moves uniformly from rest to an angular speed of 1.00 rev/s in 30.0 s. (a) Find its average angular acceleration in radians per second per second. (b) Would doubling the angular acceleration during the given period have doubled the final angular speed?
An automobile engine can produce 200Nm of torque. Calculate the angular acceleration produced if 95.0 of this torque is applied to the drive shaft, axle, and rear wheels of a car, given the following information. The car is suspended so that the wheels can turn freely. Each wheel acts like a 15.0-kg disk that has a 0.180-m radius. The walls of each tire act like a 2.00-kg annular ring that has inside radius of 0.180 m and outside radius of 0.320 m. The tread of each tire acts like a 10.0-kg hoop of radius 0.330 m. The 14.0-kg axle acts like a rod that has a 2.00-cm radius. The 30.0-kg drive shaft acts like a rod that has a 3.20-cm radius.
A rigid body with a cylindrical cross-section is released from the top of a 30 incline. It rolls 10.0 m to the bottom in 2.60 s. Find the moment of inertia of the body In terms of its mass m and radius r.