Question

A machine part has the shape of a solid uniform sphere of mass 220 g and diameter 4.50 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.

Answer 1

Answer:

The angular acceleration is 10.10 rad/s².

Explanation:

Given that,

Mass of sphere =220 g

Diameter = 4.50 cm

Friction force = 0.0200 N

Suppose we need to find its angular acceleration.

We need to calculate the angular acceleration

Using formula of torque

$\tau=f\times r$

$I\times\alpha=f\times r$

Here, I = moment of inertia of sphere

$\dfrac{2}{5}mr^2\times\alpha=f\times r$

$\alpha=\dfrac{5\times f}{2mr}$

Put the value into the formula

$\alpha=\dfrac{5\times0.0200}{2\times220\times10^{-3}\times2.25\times10^{-2}}$

$\alpha=10.10\ rad/s^2$

Hence, The angular acceleration is 10.10 rad/s².