Question

A wheel rotates with a constant angular acceleration $\alpha =0.5rad/s^2$. It has an angular velocity ${\omega }_o=-0.75rad/s$ at a time $t=0$. Consider angular position at t=0 as ${\theta }_o=0$. Find out
(a) angular speed at t=5s
(b) angular position at t=5s
(c) how much time will it take to reach angular position of ${\theta }_o={10}^{o}radian$

Answer 1

$\alpha =0.5rad/s^2$

${\omega }_0=-0.75rad/s$

First, find the time when it stops;

$\omega ={\omega }_0+\alpha t$

$0=-0.75+0.5t$

$t=2.5sec$

a) At $t=5sec$;

$\omega =0.75rad/s$ [2.5 sec is stopping time]

b) Particle will be at the same position after 5 sec.

c) $\theta ={\omega }_{0}t+\frac{1}{2}\alpha t^2$

$10=-0.75t+0.25t^2$

$40=-3t+t^2$

$t^2-3t-40=0$

$t=\frac{3\pm \sqrt{9+1600}}{2}$

$t=\frac{3+\sqrt{1609}}{2}$