In your job as a mechanical engineer you are designing a flywheel and clutch-pla

Question

In your job as a mechanical engineer you are designing a flywheel and clutch-plate system like the one in Example 10.11. Disk A is made of a lighter material than disk B, and the moment of inertia of disk A about the shaft is one-third that of disk B. The moment of inertia of the shaft is negligible. With the clutch disconnected. A is brought up to an angular speed omega_0; B is initially at rest. The accelerating torque is then removed from A, and A is coupled to B. (Ignore bearing friction.) The design specifications allow for a maximum of 2400 J of thermal energy to be developed when the connection is made. What can be the maximum value of the original kinetic energy of disk A so as not to exceed the maximum allowed value of the thermal energy?

Explanation / Answer

suppose moment of inertia of disc A is I and that of disc B is 3I, then initial kinetic energy of A-

K = I w02

when disc A is connected with disc B, heat will be developed because of friction,this energy will produce rotation in the disc B.

3I w2 = 2400

I w2 = 800

so after connection w will be same -

I w0 = I w + 3Iw

w = w0/4

so initial kinetic energy of A = 3200 joule

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