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Conservation of Angular Momentum - Controlling angular velocity on a rotating stool

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What I was demonstrating was the law of conservation of angular momentum. Now, that law says that the angular momentum of a system remains constant unless that system is acted upon by a net external torque. Now angular momentum is the product of an objects rotational inertia and its angular velocity. What I was doing by moving these masses in and out was changing the inertia of my body. With the masses out a fair amount of mass was distributed far from the axis of rotation, which was a vertical line pass that you can see through the center of my body and right through the stool. When I brought the masses in then I decreased the rotational inertia. Now, the angular momentum is the product of the rotational inertia and the angular velocity, and that remains constant as long as we don't have a net external torque. So at the beginning I had a large rotational inertia and a relatively small rotational velocity when I pulled my arms in my rotational inertia went way down and my angular velocity went way up, in order to keep the product of the two at constant. Now let's look at this again with me holding two masses in each hand. This is going to give me a greater change in rotational inertia. There you could see the changes in my angular velocity were greater, because of the greater change in rotational inertia. Now we've been saying that the law of conservation of angular momentum applies as long as no net external force acts. In fact there is a net external torque on the system; you can see as the stool rotates it will slow down because there's friction which is exerting a torque on the outer axle. But, this is small enough that you can still see the changes in angular velocity are affected by the changes in rotational inertia. This is used to good advantage by ice skaters in the high velocity spins that they achieve. They start their spin fairly slowly, but then they bring their arms and legs in very tightly and that makes them spin at a very high rate.

 



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