Show that the moment of inertia of a uniform disc of mass M and radius R about

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Show that the moment of inertia of a uniform disc of mass M and radius R about an axis through its centre and perpendicular to its surface is equal to MR2/2.
A record turntable is accelerated at a constant rate from 0 to 33 1\3 revolutions per minute in two seconds. It is a uniform disc of mass 1.5 kg and radius 13 cm. What torque is required to provide this acceleration and what is the angular momentum of the turntable at its final speed?
A mass of 0.2 kg is dropped vertically and sticks to the freely rotating turntable at a distance of 10 cm from its centre. What is the angular velocity of the turntable after the mass has been added?

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