If the arms are pulled in so the moment of inertia decreases to 1.80 kg/m2. What is the final angular speed in rad/s?
2 Answers

As external torque is absent, angular momentum (L) is conserved
moment of inertia with arms extended I1 = 2.25 kg/m2.
angular velocity w1=5.00 rad/s
Final angular momentum L2=I2w2=2.25*5=11.25 Js
moment of inertia with arms pulled I2 = 1.80 kg/m2.
final angular velocity w2= ?
Final angular momentum L2=I2w2 =1.80*w2 Js
As angular momentum is conserved,
Initial angular momentum=Li=I1w1=final angular momentum=L2=I2w2
1125=180w2
w2=1125/180=6.25 rad/s
final angular speed is 6.25 rad /s

I1W1=I2W2
I1=2.25, I2=1.80 W1=5.00 W2=???
so W2=2.25*5/1.8=6.25rad/sec