Question

A wheel which is initially at rest is subjected to a constant angular acceleration about its axis. It rotates through an angle of $15^o$ in time $t$ seconds. The increase in angle through which it rotates in the next $2t$ seconds is

• A. $90^o$
• B. $120^o$
• C. $30^o$
• D. $45^o$

Answer 1

Answer: (B)

If angular acceleration is constant, we have
$\theta ={\omega }_{0}t+\frac{1}{2}\alpha t^2$
The given $\theta =15^o$
${\omega }_0=0$
For the first conditions (time = t sec)
$15^o=0+\frac{1}{2}\alpha t^2$
$\Rightarrow$ $15^o=\frac{1}{2}\alpha t^2$ ......(i)
For the second conditions (time = t+2t sec)
${\left(\theta \right)}_1=\frac{1}{2}\alpha {\left(3t\right)}^2=\frac{1}{2}\left(\alpha \right)9t^2$ .......(ii)
So for 2t sec, $\Delta \theta ={\theta }_1-\frac{1}{2}\alpha t^2$
$\Delta \theta =9\times \frac{1}{2}\alpha t^2-\frac{1}{2}\alpha t^2$
$=8\frac{1}{2}\alpha t^2$
$=8\times 15^o=120^o$ (from equation(i))