Question

A rigid body is rotating about a vertical axis at $n$ rotations per minute. If the axis slowly becomes horizontal in $t$ seconds and the body keeps on rotating at $n$ rotations per minute then the torque acting on the body will be, if the moment of inertia of the body about axis of rotation is $I$.

• A. $Zero$
• B. $\frac{2\pi nI}{60t}$
• C. $\frac{2\sqrt{2}\pi nI}{60t}$
• D. $\frac{4\pi nI}{60t}$

Answer 1

Answer: (C)

$\frac{2\sqrt{2}\pi nI}{60t}$

Given that the axis of rotation is slowly changed to vertical to horizontal.

So, we can say that torque magnitude didn't change during the whole movement.

angular velocity,

$\omega$$=n\times$$\frac{2\pi }{60}rad{s}^{-1}$

Since , torque$=\frac{dL}{dt}${since ,l=I$\omega$}

$\Rightarrow torque=I\times \frac{\Delta \omega }{\Delta t}$

$|\overrightarrow{\omega }|=|\overrightarrow{{\omega }^{\prime }}|$

$\therefore \Delta \omega =\sqrt{{\omega }^2+{\omega }^2}=\sqrt{2}\omega$ since $\overrightarrow{{\omega }^{\prime }}\perp \overrightarrow{\omega }$

by substituting,

Torque acting on the body=$\frac{2\sqrt{2}\pi nI}{60t}$