A 15-g CD with a radius of 7.5 cm rotates with an angular speed of 40 rad/s. What is its kinetic energy?

Let's write whatt is given, and put "m" for mass, "R" for the radius of the disk, and "w" for the angular speed. We have:

m = 15g = 0.015 kg, R = 0.075m, w = 40 rad/sec

If KE is the kinetic energy of a rotaional motion, then

KE = Iw^2/2,

where "I" stands for the moment of inertia

which is (for a disk) equal to

I = mR^2/2.

Thus we have, after substitution of all numbers,

KE = m(Rw)^2 = 0.0675 J.