Write the formula for power and angular momentum in rotational motion.

A solid cylinder of mass $3\, kg$ is rolling on a horizontal surface with velocity $4\, m s^{- 1}$. It collides with a horizontal spring of force constant $200 \,N m^{-1}$. The maximum compression produced in the spring will be ............... $\mathrm{m}$

A hoop of radius $2 \;m$ weighs $100\; kg$. It rolls along a horizontal floor so that its centre of mass has a speed of $20\; cm/s$. How much work has to be done to stop it?

A $70\, kg$ man leaps vertically into the air from a crouching position. To take the leap the man pushes the ground with a constant force $F$ to raise himself The center of gravity rises by $0.5\, m$ before he leaps. After the leap the $c.g.$ rises by another $1\, m$. The maximum power delivered by the muscles is : (Take $g\, = 10\, ms^{-2}$)

A circular disc has a mass of $1\ kg$ and radius $40\ cm$. It is rotating about an axis passing through its centre and perpendicular to its plane with a speed of $10\ rev/s$. The work done in joules in stopping it would be ...... $J$

A body rolls down an inclined plane without slipping. The kinetic energy of rotation is $50 \,\%$ of its translational kinetic energy. The body is :