A particle starts rotating from rest. The instantaneous angular displacement is $\theta=3 t^3-t^2$, where $\theta$ is in radian and $t$ in s; The angular velocity at $t=1 \mathrm{~s}$ is

Applying a constant torque the speed of a flywheel is increased from 1800 rpm to 2400 rpm in 10 seconds. The number of revolutions made by the flywheel during this time is:

A bullet of momentum $p$ is fired into a door and gets embedded exactly at the center of the door. The door is 1.0 m wide and weighs 12 kg . It is hinged at one end and rotates about a vertical axis practically without friction. The angular speed of the door just after the bullet embeds into it is :

A force of $-\mathrm{F} \hat{\mathbf{i}}$ acts at the origin of the coordinate system. The torque about the point $(0,1,-1)$ is: