A machine part has the shape of a solid uniform sphere of mass 240 g and diameter 2.50 cm . It is spinning about a frictionless axle through its center, but at one point on its equator it is scraping against metal, resulting in a friction force of 0.0200 N at that point. Part A Find its angular acceleration. Let the direction the sphere is spinning be the positive sense of rotation.

Explanation:

The torque exerted on a rigid body is related to the angular acceleration by the equation

(1)

where

is the torque

I is the moment  of inertia of the body

is the angular acceleration

Here we have a solid sphere: the moment of inertia of a sphere rotating about is centre is

where

M = 240 g = 0.240 kg is the mass of the sphere

is the radius of the sphere

Substituting,

The torque exerted on the sphere is

where

F = -0.0200 N is the force of friction

r = 0.0125 m is the radius of the sphere

So

Substituting into (1), we find the angular acceleration:

they should be similar or the same