A person stands, hands at his side, on a platform that is rotating at a rate of 0.90 rev/s. If he raises his arms to a horizontal position, Fig. 8–55, the speed of rotation decreases to 0.60 rev/s.

VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko. The angular momentum of the person initially with their arms down by their side is the moment of inertia of the system times its angular velocity so we put a subscript 1 on each of those things. And this is the moment of inertia of the person/platform/system, it's all one thing. And then when they raise their arm to their sides, or sorry, like straight out horizontal, their moment of inertia will increase because there's gonna be more mass at a greater distance from the axis of rotation and so the moment of inertia will go up and then their angular velocity will change in the second case. Now since L 1 and L 2 are the same, angular momentum is conserved because there's no net torque acting on this system when they raise their arms that they are exerting a force that's internal to the system and so there's no external net torque and so angular momentum is the same. So when you have an increase in the moment of inertia when they raise their arms that has to be accompanied by a corresponding decrease in the angular velocity after they raise their arms. So L 2 is L 1 which means I 2ω 2 equals I 1ω 1 and we can figure out by what factor their moment of inertia changed by going I 2 divided by I 1 which is ω 1 over ω 2. So we can divide both sides by I 1ω 2 and we have I 2 over I 1 is ω 1 over ω 2 which is 0.90 revolutions per second divided by 0.60 revolutions per second and no need to convert this into radians per second because since the units are the same, they are gonna cancel anyway so we don't really care what the units are just so as long as they are the same. And we end up with 1.5 is the factor by which the moment of inertia changes.