Angular Velocity & Mass: Shaft Rotation & Disc Effects

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Angular velocity remains constant when a disc is attached to a rotating shaft, as long as no external torques act on the system. When a disc of 5 kg is fastened to a shaft rotating at 1500 RPM, the angular velocity of the disc also equals 1500 RPM. However, if the mass of the disc increases to 50 kg, the system's total angular momentum must be conserved, leading to a decrease in the shaft's angular velocity. The shaft will slow down to maintain the same total angular momentum with the added mass. Thus, increasing the mass of the disc affects the angular velocity of the shaft.
luk4rite
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How does the angular velocity change with increase in the mass?
For example : if there is a shaft rotating at 1500 Rpm , then if a disc of 5 kg is fastened , does the angular velocity of the disc will be same as 1500 RPM , and what happens to the RPM if the disc mass is 50Kg.
 
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luk4rite said:
How does the angular velocity change with increase in the mass?
For example : if there is a shaft rotating at 1500 Rpm , then if a disc of 5 kg is fastened , does the angular velocity of the disc will be same as 1500 RPM , and what happens to the RPM if the disc mass is 50Kg.

Momentum (angular or translational) is conserved. If the extra mass were simply attached from rest to the shaft, the mass would go from I\omega=0 to some rotational momentum greater that zero. The spinning shaft would have to lose enough angular velocity such that the sum of the rotational momenta (those of the 5 Kg mass and of the shaft) was the same.
 

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