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:

answer: the exterior temperature of commercial jet planes as they leave the stratosphere and return to the ground increases steadily.

explanation:

the lower most layer of atmosphere is troposphere which extends from 0 to 12 km above the surface of the earth. the temperature initially decreases as distance is increased from the earth's surface. commercial jets fly in lower part of the stratosphere. the stratosphere extends upto 50 km. the temperature in stratosphere starts rising again due to presence of ozone which traps the uv rays.

thus, when the planes leave the stratosphere and return to the ground, the exterior temperature increases steadily.