# Q7.12     A solid cylinder of mass  $20 kg$ rotates about its axis with angular speed $100 \: rad\: s^{-1}$. The radius of the cylinder is $0.25m$ . What is the kinetic energy associated with the rotation of the cylinder? What is the magnitude of angular momentum of the cylinder about its axis?

Firstly we will calculate moment of inertia of the solid cyliner :

$I_c\ =\ \frac{1}{2}mr^2$

$=\ \frac{1}{2}(20)(0.25)^2\ =\ 0.625\ Kg\ m^2$

So the kinetic energy is given by :

$E_k\ =\ \frac{1}{2}I\omega ^2$

$=\ \frac{1}{2}\times (6.25)\times (100) ^2$

$=\ 3125\ J$

And the angular momentum is given by :     $=\ I\omega$

$=\ 0.625\times 100$

$=\ 62.5\ Js$

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