Question

A machine part has the shape of a solid uniform sphere of mass 215 g and diameter 3.10 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.Find its angular acceleration. Let the direction the sphere is spinning be the positive sense of rotation.

Answer 1

Answer:
`\alpha =15 rad/s^2`

Step-by-step explanation:

Given

mass of sphere
`\left ( m\right )=215 g`

diameter
`\left ( d\right )=3.10 cm`

Friction Force=0.02 N

here friction force will provide torque

thus
`f_r* r=I* \alpha`

`0.02* r=(2mr^2)/(5)* \alpha`

`\alpha =(0.02* 5* r)/(2* m* r^2)`

`\alpha =(5* 0.02)/(2* 0.215* 1.55* 10^(-2))`

`\alpha =15 rad/s^2`