Question

For a rotating object experiencing no net external torque, what happens to the rate of rotation if the moment of inertia of the object decreases by a factor of 2

Answer 1

Answer:

The rate of rotation increases by a factor of 2.

Explanation:

Answer 2

The rate of rotation will become two times as the moment of inertia will be decreased by 2 times for the constant torque.

What will be the rate of rotation?

The torque for the rotating body will be given by the formula

$T= I\alpha$

Here,

T= Torque

I= Moment of inertia

$\alpha=$ Angular acceleration / Rate of rotation

Now from the question, it is given that a rotating object experiencing no net external torque, what happens to the rate of rotation if the moment of inertia of the object decreases by  2 times.

Here moment of inertia will be   $I'=\dfrac{I}{2}$

So the formula will become

$T= \dfrac{I}{2} \times \alpha$

Now for making the Torque to be constant the acceleration should be two times  $\alpha'=2\alpha$

So for constant torque

$T= \dfrac{I}{2} \times 2\alpha$

Thus The rate of rotation will become two times as the moment of inertia will be decreased by 2 times for the constant torque.

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