The angular velocity of a rotor about its fixed axis varies according to the law (in…

PHYSICS · Subjective · A Level · Physics · Engineering physics · Engineering physics

Problem

The angular velocity of a rotor about its fixed axis varies according to the law

\omega = 2t + 3

(in rad s

^{-1}

) for

0 \le t \le 4\,\text{s}

. Immediately after

t = 4\,\text{s}

it is subjected to a constant angular deceleration of

1.5\,\text{rad s}^{-2}

until it comes to rest. Answer the following: (a) Determine the angular displacement produced during the first

4\,\text{s}

. (b) Find the time taken, measured from

t = 4\,\text{s}

, for the rotor to come to rest. (c) Calculate the additional angular displacement during the retardation phase. (d) Sketch qualitative

\theta

–

t

and

\omega

–

t

graphs for the entire motion from

t = 0

until rest, indicating clearly the point corresponding to

t = 4\,\text{s}