A uniform sphere with mass M and radius R is rotating with angular speed wi about a frictionless axle along a diameter of the sphere. The sphere has rotational kinetic energy K1. A thin-walled hollow sphere has the same mass and radius as the uniform sphere. It is also rotating about a fixed axis along its diameter. Part A In terms of wi, what angular speed must the hollow sphere have if its kinetic energy is also K, the same as for the uniform sphere? Express your answer in terms of wi. wh = 0.7746

A uniform sphere with mass M and radius R is rotating with angular speed wi about a frictionless axle along a diameter of the sphere. The sphere has rotational kinetic energy K1. A thin-walled hollow sphere has the same mass and radius as the uniform sphere. It is also rotating about a fixed axis along its diameter. Part A In terms of wi, what angular speed must the hollow sphere have if its kinetic energy is also K, the same as for the uniform sphere? Express your answer in terms of wi. wh = 0.7746

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Rigid Body

A rigid body is an object which does not change its shape or undergo any significant deformation due to an external force or movement. Mathematically speaking, the distance between any two points inside the body doesn't change in any situation.

Rigid Body Dynamics

Rigid bodies are defined as inelastic shapes with negligible deformation, giving them an unchanging center of mass. It is also generally assumed that the mass of a rigid body is uniformly distributed. This property of rigid bodies comes in handy when we deal with concepts like momentum, angular momentum, force and torque. The study of these properties – viz., force, torque, momentum, and angular momentum – of a rigid body, is collectively known as rigid body dynamics (RBD).

Question

A uniform sphere with mass M and radius R is rotating with
angular speed wi about a frictionless axle along a diameter
of the sphere. The sphere has rotational kinetic energy K1. A
thin-walled hollow sphere has the same mass and radius as
the uniform sphere. It is also rotating about a fixed axis along
its diameter.
Part A
In terms of wi, what angular speed must the hollow sphere have if its kinetic energy is also K1, the same as for the uniform sphere?
Express your answer in terms of wi.
?
wh = 0.7746

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