A diver can change his moment of inertia by drawing his arms and legs close to h

Question

A diver can change his moment of inertia by drawing his arms and legs close to his body in the tuck position. A certain diver has a moment of inertia of 24.0 kgm2 in the straight position. In the tucked position his moment of inertia is 8.00 kgm2 . After he leaves the diving board (standing straight and with some unknown angular velocity), he pulls himself into a ball (the tuck position) as closely as possible and makes 2.00 complete rotations in 1.33s. What was his angular velocity when he left the diving board?

Explanation / Answer

Here ,

moment of inertia in straight condition , I1 = 24 Kg.m^2

moment of inertia in tucked in position , I2 = 8 Kg.m^2

initial angular speed , w2 = 2*2pi/1.33

w2 = 9.45 rad/s

Now , let the angular velocity when he left the board is w1 ,

Using conservation of angular momentum ,

I1 * w1 = I2 * w2

24 * w1 = 8 * 9.45

w1 = 3.15 rad/s

his angular velocity when he left the diving board is 3.15 rad/s

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