Question

A constant external torque $\tau$ acts for a very brief period $\Delta t$ on a rotating system having moment of inertial $I$.

• A. The angular momentum of the system will change by $\tau \Delta t$.
• B. The angular velocity of the system will change by $\frac{\tau \Delta t}{I}$.
• C. If the system of initially at rest, will acquire rotational kinetic energy $\frac{{\left(\tau \Delta t\right)}^2}{2I}$.
• D. The kinetic energy of the system will change by $\frac{{\left(\tau \Delta t\right)}^2}{I}$

Answer 1

Answer: (A), (B), (C)

The correct options are
A The angular momentum of the system will change by $\tau \Delta t$.
B The angular velocity of the system will change by $\frac{\tau \Delta t}{I}$.
C If the system of initially at rest, will acquire rotational kinetic energy $\frac{{\left(\tau \Delta t\right)}^2}{2I}$.

Let $L=$ angular momentum$\tau =\frac{dL}{dt}\Rightarrow dL=\tau dt$ For constant torque $\Delta L=\tau \Delta t=I\Delta \omega$ $\Rightarrow \Delta L=I\omega$ (if ${\omega }_1=0$Rotational kinetic energy $=\frac{1}{2}I{\omega }^2=\frac{{\left(\Delta L\right)}^2}{2I}$$\therefore \left(A\right),\left(B\right)$ and $\left(C\right)$