1. explain how you can change a object's angular frequency.?

Question

2. why does a gymnast appear to be floating on air when she raises her arms above her head in a leap?
3. The rotational velocity of a merry-go-round in increased at a constant rate from 1.5/s to 3.5/s. What is the rotational acceleration of the merry-go-round?

Answer 1

1. Apply torque, or if you can't do that, use conservation of angular momentum, I*omega, and change I, the moment of inertia like a skater pulling her arms in close.

2. Her center of mass will follow a proper trajectory. If she moves her arms, her center of mass will move with respect to her body.

3. Those rotation rates: 1.5 and 3.5 RADIANS/s? I'll assume so. Let me use W for omega.
Wf = Wo + alpha*t
alpha will be in radians/s^2