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.

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;

                                    ........ (1)                              

Here, I is the moment of inertia, K is the rotational kinetic energy and is the angular velocity.

The rotational kinetic energy for second object is as follows;

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.

                              ......... (2)

From (1) and (2),

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