Question

A rigid body rotates about a fixed axis with variable angular velocity equal to $(a-bt)$ 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. $\frac{a^2}{2b}$
• C. $\frac{a^2}{4b}$
• D. $\frac{a^2}{2b^2}$

Answer 1

Answer: (B)

$\omega =a-bt$ (Given)
At time $t=0,\omega ={\omega }_0=a$
$\alpha =\frac{d\omega }{dt}=\frac{d}{dt}(a-bt)=-b$
${\omega }^2={\omega }_0^2+2\alpha \theta$