Question

Two objects have the same rotational kinetic energy. Object one has twice the moment of inertia than the second. The angular velocity of the first object is _________ times the angular velocity of the second object.

Answer 1

Answer:

The angular velocity of the first object is twice times the angular velocity of the second object.

Explanation:

The expression for the rotational kinetic energy for first object is as follows;

$K=\frac{1}{2}I \omega^{2}$                                     ........ (1)                              

Here, I is the moment of inertia, K is the rotational kinetic energy and $\omega^{2}$ is the angular velocity.

The rotational kinetic energy for second object is as follows;

$K'=\frac{1}{2}I' \omega'^{2}$

According to given condition, two objects have the same rotational kinetic energy. Object one has twice the moment of inertia than the second.

Suppose, I'=2I.

$K'=\frac{1}{2}(2I) \omega'^{2}$                               ......... (2)

From (1) and (2),

$\frac{1}{2}I \omega^{2}=\frac{1}{2}(2I) \omega'^{2}$

$\omega^{2}=(2) \omega'^{2}$

$\omega=2\omega'$

Therefore, the angular velocity of the first object is twice the angular velocity of the second object.