Question

A wheel is making revolutions about its axis with uniform angular acceleration. Starting from rest it reaches $100rev/sec$ in $4$ seconds. Then the angle rotates during these $4$ seconds

• A. $100\pi$ rad
• B. $200\pi$ rad
• C. $300\pi$ rad
• D. $400\pi$ rad

Answer 1

The correct option is D $400\pi$ rad

given values initial velocity ${\omega }_1=0$

angular velocity at ${\omega }_2=100rev/s=200\ast \pi rad/s=628rad/s$

$t=4s$

angular acceleration, $\alpha =\frac{{\omega }_2-{\omega }_1}{t}=\frac{(628-0)}{4}=157rad/s^2$

angle rotated = $\frac{({\omega }_2^2-{\omega }_1^2)}{2\alpha }=\frac{\left({628}^2\right)}{2\ast 157}=1256rad=400\pi rad$