Question

A wheel is making Revolution about axis with uniform angular acceleration, Starting from rest, it reaches $100rev/sec$ in $4seconds$. Find the angular rotated during these four seconds.

• A. $200\pi rad/sec$
• B. $400\pi rad/sec$
• C. $600\pi rad/sec$
• D. $800\pi rad/sec$

Answer 1

The correct option is B $400\pi rad/sec$

We know that angular velocity $\left(\omega \right)=2\pi f$

Frequency $\left(f\right)=100rev/sec$

$⟹\omega =200\pi rad/s$

angular acceleration $\left(\alpha \right)=\frac{\omega }{t}=\frac{200\pi }{4}=50\pi rad/s^2$

angle rotated$\left(\theta \right)={\omega }_{o}t+\frac{1}{2}\alpha t^2$

${\omega }_o=0$

$⟹\theta =\frac{1}{2}50\pi \times 4^2=400\pi rad$