Difficult Dynamics/Circular Motion Question

LouN1997

A disc of mass m, radius R and angular velocity omega, has its mass uniformly distributed over its area. Calculate the total kinetic enegy of the disc as follows:

i) write down the mass of the disc contained between radius r and radius r + dr
ii) write down the speed of this mass
iii) calculate the kinetic energy of this mass
iv) calculate the total kinetic energy of the whole disc by integrating the previous result with respect to r between the limits r=0 and r=R

I have worked out the mass in part i to be drm but apart from that I do not know how to do the other parts