A hollow sphere of mass M and radius R = 0.15 m, with rotational inertia I = 0.040kg · m? about a line through its center of mass, rolls without slipping up a surface inclinedat 0 = 30° to the horizontal. At a certain position, say at a height h1 from the ground, thesphere's total kinetic energy (its center of mass kinetic energy plus its rotational kineticenergy) is 20 J. (Hint: The moment of inertia of such a halo sphere is I = MR². Thetranslational speed of a point on the surface of the sphere is the same as the speed of thecenter of mass of the sphere)(a) What ratio of this total kinetic energy is rotational?(b) What is the speed of the center of mass of the sphere at this position?When the sphere has moved d = 1 m up the incline from this (initial) position, usingconservation of energy, find(c) its total kinetic energy, and(d) the speed of its center of massd = 1 m

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A hollow sphere of mass M and radius R = 0.15 m, with rotational inertia I = kg · m2 about a line through its center of mass, rolls without slipping up a surface inclined at 0 = 30° to the horizontal. At a certain position, say at a height hi from the ground, the sphere's total kinetic energy (its center of mass kinetic energy plus its rotational kinetic energy) is 20 J. (Hint: The moment of inertia of such a halo sphere is I = translational speed of a point on the surface of the sphere is the same as the speed of the center of mass of the sphere) 0.040 MR. The (a) What ratio of this total kinetic energy is rotational? (b) What is the speed of the center of mass of the sphere at this position? When the sphere has moved d = 1 m up the incline from this (initial) position, using conservation of energy, find (c) its total kinetic energy and (d) the speed of its center of mass d = 1m R

A hollow sphere of mass M and radius R = 0.15 m, with rotational inertia I = kg · m2 about a line through its center of mass, rolls without slipping up a surface inclined at 0 = 30° to the horizontal. At a certain position, say at a height hi from the ground, the sphere's total kinetic energy (its center of mass kinetic energy plus its rotational kinetic energy) is 20 J. (Hint: The moment of inertia of such a halo sphere is I = translational speed of a point on the surface of the sphere is the same as the speed of the center of mass of the sphere) 0.040 MR. The (a) What ratio of this total kinetic energy is rotational? (b) What is the speed of the center of mass of the sphere at this position? When the sphere has moved d = 1 m up the incline from this (initial) position, using conservation of energy, find (c) its total kinetic energy and (d) the speed of its center of mass d = 1m R

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 39P

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