Physics - Rotation Question with Solution | TestHub

The angle rotated by a body in the $n^{\text{th}}$ second under uniform angular acceleration is given by the kinematic equation:

${\theta }_n={\omega }_0+\frac{\alpha }{2}(2n-1)$

Since the disc starts from rest, the initial angular velocity ${\omega }_0=0$.

The angle rotated in the $2^{\text{nd}}$ second ($n=2$) is:

$\theta =\frac{\alpha }{2}(2(2)-1)=\frac{3\alpha }{2}$

The angle rotated in the $3^{\text{rd}}$ second ($n=3$) is:

${\theta }^1=\frac{\alpha }{2}(2(3)-1)=\frac{5\alpha }{2}$

Taking the ratio of the two angles:

$\frac{\theta }{{\theta }^1}=\frac{\frac{3\alpha }{2}}{\frac{5\alpha }{2}}=\frac{3}{5}$

Answer: $3:5$