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:

A solid cylinder of mass $$2 \mathrm{~kg}$$ and radius $$0.2 \mathrm{~m}$$ is rotating about its own axis without friction with angular velocity $$5 \mathrm{~rad} \mathrm{s}^{-1}$$. A particle of mass $$1 \mathrm{~kg}$$ moving with a velocity of $$5 \mathrm{~ms}^{-1}$$ strikes the cylinder and sticks to it as shown in figure.

The angular velocity of the system after the particle sticks to it will be