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.

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air exerts forces on falling objects near earth’s surface.

explanation:

the term 'free falls' refer to object that are falling towards the earth, in a situation in which gravity is the only force acting on the object.

for an object in free fall, the acceleration is constant (g, the gravitational acceleration), and so the velocity of the object constantly increases.

for objects near earth's surface, there is always another force acting on the object: the resistance due to the air. this force is opposed to the direction of fall of the object, and it is proportional to the velocity of the object, so as the object falls down, this force increases up to a point when it balances the force of gravity, and the object continues its motion at constant velocity (called terminal velocity). since in this case gravity is not the only force acting on the object, we are not in a situation of free fall.