Question

A rotating wheel has a constant angular acceleration. It has an angular velocity of 5.0 rad/s at time t=0 s, and 3.0 s later has an angular velocity of 9.0 rad/s. What is the angular displacement of the wheel during the 3.0-s interval?
(a) 15 rad
(b) 21 rad
(c) 27 rad
(d) There is not enough information given to determine the angular displacement.

Answer 1

Answer:

Angular displacement will be 21 rad

So option (b) will be correct answer

Explanation:

We have given initial angular velocity $\omega _i=5rad/sec$

Final angular velocity $\omega _f=9rad/sec$

Time t = 3 sec

Angular acceleration is given by $\alpha =\frac{\omega _f-\omega _i}{t}=\frac{9-5}{3}=1.333rad/sec^2$

Now angular displacement is given by $\Theta =\omega _it+\frac{1}{2}\alpha t^2=5\times 3+\frac{1}{2}\times 1.333\times 3^2=21rad$

So option (b) will be correct option