A wheel is rotating freely with an angular speed ω on a shaft. The moment of inertia of the wheel is I and the moment of inertia of the shaft is negligible. Another wheel of moment of inertia 3 I init

Question

A wheel is rotating freely with an angular speed ω on a shaft. The moment of inertia of the wheel is I and the moment of inertia of the shaft is negligible. Another wheel of moment of inertia 3 I initially at rest is suddenly coupled to the same shaft. The resultant fractional loss in the kinetic energy of the system is:

TestHub · Accepted Answer

From angular momentum conservation I ω + 0 = I ω C + 3 I ω C ω c = ω 4 Loss of kinetic energy = 1 2 I ω 2 - 1 2 ( I + 3 I ) ω 4 2 = 1 2 I ω 2 - 1 2 I ω 2 4 = 3 8 I ω 2 Fractional loss = 3 4

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