A diver begins a high dive with an angular velocity of 6.3 rad/s. By tucking himself into a ball, he decreases his moment of inertia by a factor of 9.0. What is his new angular speed?

angular momentum is conserved:

angmom= I w If I goes down to 1/5, w increases by 5.

To find the new angular speed of the diver, we need to use the conservation of angular momentum. Angular momentum is given by the equation:

L = I * ω

Where:
L is the angular momentum,
I is the moment of inertia,
ω (omega) is the angular velocity.

Since the diver decreases his moment of inertia by a factor of 9.0, the new moment of inertia (I') will be 1/9.0 times the initial moment of inertia (I).

So, I' = (1/9.0) * I

Since angular momentum is conserved, we can equate the initial angular momentum (L) to the final angular momentum (L'):

I * ω = I' * ω'

Substituting the values we have:

I * ω = (1/9.0) * I * ω'

Simplifying the equation, we can cancel out the moment of inertia (I):

ω = (1/9.0) * ω'

Now we can solve for ω', the new angular speed of the diver:

ω' = 9.0 * ω

Substituting the given value ω = 6.3 rad/s, we can calculate the new angular speed:

ω' = 9.0 * 6.3 rad/s = 56.7 rad/s

Therefore, the diver's new angular speed is 56.7 rad/s.