Question

A chain is wrapped around a pulley and pulled
with a force of 16.0 N. The pulley has a radius of
0.20 m. The pulley's rotational speed increases
from 0.0 to 17.0 rev/min in 5.00 s. What is the
moment of inertia of the pulley?​

Answer 1

Given:

A chain is wrapped around a pulley and pulled with a force of 16.0 N. The pulley has a radius of 0.20 m. The pulley's rotational speed increases from 0.0 to 17.0 rev/min in 5.00 s.

To find:

Moment of Inertia of pulley?

Calculation:

We know that :

$\rm \tau = I \times \alpha$

$\rm \implies \: F \times r = I \times \alpha$

$\rm \implies \: F \times r = I \times \bigg( \dfrac{ \omega2 - \omega1}{t} \bigg)$

$\rm \implies \: 16 \times 0.2 = I \times \bigg \{\dfrac{(17 - 0) \times \frac{2\pi}{60} }{5} \bigg \}$

$\rm \implies \: 3.2 = I \times \bigg \{\dfrac{34\pi}{300} \bigg \}$

$\rm \implies \: I = 8.98 \: kg \: {m}^{2}$

So, moment of inertia of the body is 8.98 kgm².