Nonuniform ball. In the figure below, a ball of mass M and radius R rolls smooth

Question

Nonuniform ball. In the figure below, a ball of mass M and radius R rolls smoothly from rest down a ramp and onto a circular loop of radius 0.54 m. The initial height of the ball is h = 0.37 m. At the loop bottom, the magnitude of the normal force on the ball is 2.00Mg. The ball consists of an outer spherical shell (of a certain uniform density) that is glued to a central solid sphere (of a different uniform density). The rotational inertia of the ball can be expressed in the general form I =?MR2, but ? is not 0.4 as for a ball with a single uniform density. Determine ?.

Nonuniform ball. In the figure below, a ball of mass M and radius R rolls smoothly from rest down a ramp and onto a circular loop of radius 0.54 m. The initial height of the ball is h = 0.37 m. At the loop bottom, the magnitude of the normal force on the ball is 2.00Mg. The ball consists of an outer spherical shell (of a certain uniform density) that is glued to a central solid sphere (of a different uniform density). The rotational inertia of the ball can be expressed in the general form I =?MR2, but ? is not 0.4 as for a ball with a single uniform density. Determine ?.

Explanation / Answer

The height energy lost = the KE gained

M . g . h = 1/2 . M . v^2 + 1/2 . I . w^2

I =

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