Question

A fly wheel is accelerated uniformly from rest and rotates through $5\text{rad}$ in the first second. The angle rotated by the fly wheel in the next second, will be :

• A. $20\text{rad}$
• B. $30\text{rad}$
• C. $15\text{rad}$
• D. $7.5\text{rad}$

Answer 1

The correct option is C $15\text{rad}$

Given,

Initial velocity, $\omega =0$
Initial angle of rotation, ${\theta }_1=5\text{rad}$ in time $t_1=1\text{s}$

Using, $\theta =\omega t+\frac{1}{2}\alpha t^2$

${\theta }_1=5=0+\frac{1}{2}\alpha \times 1^2$

$\Rightarrow \alpha =10{\text{rad/sec}}^2$

Total angle rotated during the first two seconds,

${\theta }_2=0+\frac{1}{2}\times 10\times 2^2=20\text{rad}$

$\therefore$ Angle rotated during the 2nd second
$\theta =20-5=15\text{rad}$

Hence, $\left(B\right)$ is the correct answer.