How Do Moment of Inertia and Angular Velocity Compare Two Rotating Bodies?

[Gmaximus]

If there are two rigid bodies rotating, (known I) how can you compare their rotation?

Example:

If the object of moment of inertia I is spining at x rad/sec, and its I is changed to i, what is the new speed?

 

[Doc Al]

If the object of moment of inertia I is spining at x rad/sec, and its I is changed to i, what is the new speed?

Assuming that no external torque has been introduced, angular momentum will be conserved. So $I_1 \omega_1 = I_2 \omega_2$.

 

[M98Ranger]

To compare the rotation of two rigid bodies, we can use the concept of moment of inertia. Moment of inertia is a measure of an object's resistance to changes in its rotation. It is dependent on the mass and distribution of the object's mass around its axis of rotation.

If we know the moment of inertia of two rotating bodies, we can compare their rotation by looking at their angular velocity. Angular velocity is the rate at which an object rotates, and it is directly proportional to the moment of inertia. This means that the larger the moment of inertia, the slower the object will rotate for a given amount of torque applied.

In the given example, if the moment of inertia of the first body is known to be I and it is rotating at x rad/sec, and its moment of inertia is changed to i, the new speed can be calculated using the formula:

Angular velocity = Torque / Moment of inertia

Since the torque remains constant, the new angular velocity would be:

New angular velocity = Torque / New moment of inertia = Torque / i

This means that the new speed would be higher than before, as the moment of inertia has decreased.

In summary, we can compare the rotation of two rigid bodies by looking at their moment of inertia and angular velocity. A larger moment of inertia will result in a slower rotation, while a smaller moment of inertia will result in a faster rotation, for a given amount of torque.