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…

Question

A wheel is rotating freely with an angular speed &#969; 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:

Aicharya · Accepted Answer

From angular momentum conservation I &#969; + 0 = I &#969; C + 3 I &#969; C &#969; c = &#969; 4 Loss of kinetic energy = 1 2 I &#969; 2 - 1 2 ( I + 3 I ) &#969; 4 2 = 1 2 I &#969; 2 - 1 2 I &#969; 2 4 = 3 8 I &#969; 2 Fractional loss = 3 4

A wheel is rotating freely with an angular speed ω on a shaft. The moment of inertia of the wheel is I…

Solution

A wheel is rotating freely with an angular speed &#969; on a shaft. The moment of inertia of the wheel is I…

Solution

A wheel is rotating freely with an angular speed ω on a shaft. The moment of inertia of the wheel is I…