angular momentum is conserved:
angmom= I w If I goes down to 1/5, w increases by 5.
angmom= I w If I goes down to 1/5, w increases by 5.
L = I * ฯ
Where:
L is the angular momentum,
I is the moment of inertia,
ฯ (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 * ฯ = I' * ฯ'
Substituting the values we have:
I * ฯ = (1/9.0) * I * ฯ'
Simplifying the equation, we can cancel out the moment of inertia (I):
ฯ = (1/9.0) * ฯ'
Now we can solve for ฯ', the new angular speed of the diver:
ฯ' = 9.0 * ฯ
Substituting the given value ฯ = 6.3 rad/s, we can calculate the new angular speed:
ฯ' = 9.0 * 6.3 rad/s = 56.7 rad/s
Therefore, the diver's new angular speed is 56.7 rad/s.