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:

wind moving at higher speeds will transfer more energy to the water, resulting in stronger waves.