A flywheel at rest is to reach an angular velocity of 24 rad/s in 8 second with constant angular acceleration. The total angle turned through during this interval is

Options

A. 24 rad
B. 48 rad
C. 72 rad
D. 96 rad

Answer

D

Explanation

Given, `omega_(0) = 0, omega = 24` rad/s, `f = 8s`
From the relation , `omega = omega_(0) + alphat`
`rArr alpha = (omega - omega_(0))/(t)`
Subsituting the given values, we get
`alpha = 28//8 = 3 "rad"//s^(2)`
Also, `theta = omega_(0)t + 1/2 alphat^(2) = 0 +1/2 xx 3 xx (8)^(2)`
`= (3 xx 64)/(2) = 96` rad