Question

A wheel is rotating about a fixed axis with angular velocity decreasing at a constant rate. If angular velocity becomes $50\%$ of its initial value by making ${}^{\prime }{n}^{\prime }$ rotations , then how many more rotations, will it makes to comes to rest?

• A. $\frac{n}{2}$
• B. $\frac{n}{3}$
• C. $\frac{n}{4}$
• D. $\frac{n}{6}$

Answer 1

The correct option is B $\frac{n}{3}$

${\omega }_1^2-{\omega }_2^2=2\alpha \theta$

$(\frac{\omega }{2}{)}^2-{\omega }^2=2\alpha 2\pi n$

$\alpha =\frac{3{\omega }^2}{16n\pi }$

$0-(\frac{\omega }{2}{)}^2=2\alpha 2\pi n^{\prime }$

$n^{\prime }=\frac{n}{3}$