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.