Afigure skater rotating at 5.00 rad/s with arms extended has a moment of inertia of 2.25 kgâ·m2. if the arms are pulled in so the moment of inertia decreases to 1.80 kgâ·m2

what is:
a) the final angular speed?
b) the initial and final kinetic energy?

a) 6.25 rad/s

The law of conservation of angular momentum states that the angular momentum must be conserved.

The angular momentum is given by:

where

I is the moment of inertia

is the angular speed

Since the angular momentum must be conserved, we can write

where we have

is the initial moment of inertia

is the initial angular speed

is the final moment of inertia

is the final angular speed

Solving for , we find

b) 28.1 J and 35.2 J

The rotational kinetic energy is given by

where

I is the moment of inertia

is the angular speed

Applying the formula, we have:

- Initial kinetic energy:

- Final kinetic energy:

c.is a substance that requires a small amount of energy per gram to raise its temperature; has strong cohesive forces between molecules.

explanation:

a colorless, transparent, odorless liquid that forms the seas, lakes, rivers, and rain and is the basis of the fluids of living organisms.