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Physics Problem

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?

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1 Answer

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.