Question

When a diver gets into a tuck position by pulling in her arms and legs, she increases her angular speed. before she goes into the tuck position, her angular velocity is 5.5 rad/s and she has a moment of inertia of 2.0 kg · m2. once she gets into the tuck position, her angular speed is 11.5 rad/s. determine her moment of inertia when she is in the tuck position. assume the net torque on her is zero?

Answer 1

Before she gets into a tuck position, distribution of mass of her body about axis of rotation increases. As a result, her angular velocity decreases. When a diver gets into a tuck position, distribution of mass of her body about axis of rotation becomes less. As a result, her angular velocity increases. During this whole time, there is only one force acting on her body which is her own weight "mg". The net torque acting on her all the time is zero because "mg" force passes through this axis of rotation which causes no moment. Since there is no torque acting on her body, angular momentum should remain constant ( before tuck and after tuck)
Angular momentum is defined as,
L = Iω
Since net torque is zero,
Li = Lf ........... (Li = initial angular momentum, Lf = final angular momentum)
(Iω)i= (Iω)f

Ii = 2.0 kg · m² , ωi = 5.5 rad/s, ωf = 11.5 rad/s.
From given, find If.