Question

A rigid body is rotating with variable angular velocity ω = (28 – 4t) radian/s, the total angle rotated by it before coming to rest will be
(1) 98 radians
(2) 96 radians
(3) 196 radians
(4) 94 radians

Answer 1

$$\begin{gathered} \mathrm{Time}\mathrm{taken}\mathrm{to}\mathrm{come}\mathrm{to}\mathrm{rest}: \\ \mathrm{\omega }=0 \\ 28-4\mathrm{t}=0 \\ \mathrm{t}=7\mathrm{s} \\ \mathrm{Angular}\mathrm{acceleration}: \\ \mathrm{\alpha }=\frac{\mathrm{d\omega }}{\mathrm{dt}} \\ =\frac{\mathrm{d}}{\mathrm{dt}}\left(28-4\mathrm{t}\right) \\ =-4\mathrm{rad}/{\mathrm{s}}^2 \\ \mathrm{Angle}: \\ \mathrm{\theta }={\mathrm{\omega }}_0\mathrm{t}+\frac{1}{2}{\mathrm{\alpha t}}^2 \\ =\left(28-4\times 0\right)7+\frac{1}{2}\times -4\times 7^2 \\ =196-98 \\ =98\mathrm{radians} \\ \mathbf{Ans}\mathbf{:}\mathbf{}\mathbf{Option}\mathbf{-}\mathbf{1} \end{gathered}$$