Angular Velocity & Mass: Shaft Rotation & Disc Effects

In summary, as mass is added to a rotating shaft, the angular velocity decreases in order to maintain the conservation of momentum. The amount of decrease depends on the added mass and the initial angular velocity.
  • #1
luk4rite
1
0
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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  • #2
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[itex]\omega[/itex]=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.
 

1. What is angular velocity?

Angular velocity is a measure of how fast an object is rotating around a fixed point. It is typically measured in radians per second or degrees per second.

2. How is angular velocity calculated?

Angular velocity is calculated by dividing the change in angular displacement (in radians or degrees) by the change in time. This is represented by the formula ω = Δθ / Δt.

3. How does mass affect angular velocity?

The mass of an object does not directly affect its angular velocity. However, the distribution of mass (i.e. how the mass is spread out) can affect the object's moment of inertia, which in turn can affect its angular velocity.

4. What is the relationship between shaft rotation and angular velocity?

Shaft rotation is a type of circular motion that is characterized by a constant angular velocity. This means that the rate of change of the angle of rotation remains constant, regardless of the position of the rotating object.

5. How does a disc affect angular velocity?

A disc can affect angular velocity by changing the moment of inertia of the rotating object. A disc with a larger radius or greater mass will have a larger moment of inertia, which will require more torque to produce the same angular velocity as a disc with a smaller radius or less mass.

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