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.