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:$\alpha =15 rad/s^2$

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 $f_r\times r=I\times \alpha$

$0.02\times r=\frac{2mr^2}{5}\times \alpha$

$\alpha =\frac{0.02\times 5\times r}{2\times m\times r^2}$

$\alpha =\frac{5\times 0.02}{2\times 0.215\times 1.55\times 10^{-2}}$

$\alpha =15 rad/s^2$