Jane who is practicing gymnastics performs an aerial maneuve

Jane who is practicing gymnastics, performs an aerial maneuver. While in a tucked position, as shown in Figure A, she rotates about her center of mass at a rate of 5.55 rad/s. Her rotational inertia about this axis is 20.3 kg middot m^2. A short time later Jane is in the straight position, as shown in Figure B. If the rotational inertia about her center of mass in this position is 31.3 kg middot m^2, what is her rotational speed?

Solution

According the given problem,

Angular momentum = I *

Initial Angular momentum = 20.3 * 5.55 = 112.665

and Final angular momentum = 31.3 * _f

Using Conservation of angular momentum principle:

31.3 * _f = 112.665

_f = 112.665/31.3

_f = 3.599

This is approximately 3.6 rad/s.