A uniform solid sphere of radius r is placed on the inside surface of a hemisphe

Question

A uniform solid sphere of radius r is placed on the inside surface of a hemispherical bowl with radius R. The sphere is released from rest at an angle ? to the vertical and rolls without slipping (see figure below). Determine the angular speed of the sphere when it reaches the bottom of the bowl. (Use any variable or symbol stated above along with the following as necessary: g for the acceleration of gravity.)

A uniform solid sphere of radius r is placed on the inside surface of a hemispherical bowl with radius R. The sphere is released from rest at an angle ? to the vertical and rolls without slipping (see figure below). Determine the angular speed of the sphere when it reaches the bottom of the bowl. (Use any variable or symbol stated above along with the following as necessary: g for the acceleration of gravity.)

Explanation / Answer

M x g x R(1-cos) = 0.5 m x v^2 + 0.5 Ix w^2

v = rw

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