Question

A rigid body rotates about a fixed axis with variable angular velocity equal to $(a-b t)$ at time $t$ where $a$ and $b$ are constants. The angle through which it rotates before it comes to rest is

• A. $\frac{a^{2}}{b}$
• B. $\frac{a^{2}}{2 b}$
• C. $\frac{a^{2}}{4 b}$
• D. $\frac{a^{2}}{2 b^{2}}$

Answer 1

Answer: (B)

$ \omega=a-b t \,\,\,\,\, $ (Given)
At time $t=0, \omega=\omega_{0}=a$
$\alpha=\frac{d \omega}{d t}=\frac{d}{d t}(a-b t)=-b$
$\omega^{2}=\omega_{0}^{2}+2 \alpha \theta$