Q: A wheel which is initially at rest is subjected to a constant angular acceleration about its axis. It rotates through an angle of 15° in time t sec. Then how much it rotates in the next 2t sec.

Sol: If angular acceleration is constant, we have

$\large \theta = \omega_0 t + \frac{1}{2}\alpha t^2$

$\large 15^o = \frac{1}{2}\alpha t^2 $ …(i)

for the second condition (time = 3t sec)

$\large \theta’ = \frac{1}{2}\alpha (3t)^2 $

$\large \theta’ = 9 \times 15 = 135^o $ …(ii)

$\large \Delta \theta = \theta’ – \theta $

$\large \Delta \theta = 135^o – 15^o = 120^o $