A flywheel rotates with a uniform angular acceleration. Its angular velocity increases from 20 `pi` rad/s to 40 `pi` rad/s in 10 seconds. How many rotations did it make in this period?

Options

A. 80
B. 100
C. 120
D. 150

Answer

D

Explanation

As `omega = omega_(0) + alpha t implies 40 pi = 20 pi + alpha xx 10`
or `alpha = 2pi "rad/s"^(2)`
As `omega^(2) - omega_(0)^(2) = 2 alpha theta implies (40pi)^(2) - (20pi)^(2) = 2 xx 2 pi theta`
or `theta = (1200 pi^(2))/(4 pi) = 300 pi`
No. of rotations completed = `(theta)/(2pi) = (300 pi)/(2pi) = 150`