A student sits on a pivoted stool while holding a pair of weights. The stool is free to rotate about a vertical axis with negligible friction. If he suddenly releases the weights, his angular speed will( ).
The answer is “remain the same”. I want to know why. I think the mass becomes less so the moment of inertia becomes less, so the angular speed increases. What is wrong with my idea?
The answer is “remain the same”. I want to know why. I think the mass becomes less so the moment of inertia becomes less, so the angular speed increases. What is wrong with my idea?
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There is a difference between "releasing the weights" and " bringing the weights closer to his body"
If you release the weights then they must contain the same angular momentum that they did immediately prior to release. You have not given them any force to alter this.
In the same way, if all you do is release the weights then they have exerted no forces on you.
Consequently, you also have the same angular momentum that you did immediately prior to release.
And you also have the same moment of inertia that you did prior to the release.
Hence YOU must have the same angular velocity that you did prior to the release.
Now the weights are a different story.
As they get further from you, their moment of inertia increases so their angular velocity decreases.
But this cannot affect you. You are not touching the weights nor are connected to them by any other means.
If you release the weights then they must contain the same angular momentum that they did immediately prior to release. You have not given them any force to alter this.
In the same way, if all you do is release the weights then they have exerted no forces on you.
Consequently, you also have the same angular momentum that you did immediately prior to release.
And you also have the same moment of inertia that you did prior to the release.
Hence YOU must have the same angular velocity that you did prior to the release.
Now the weights are a different story.
As they get further from you, their moment of inertia increases so their angular velocity decreases.
But this cannot affect you. You are not touching the weights nor are connected to them by any other means.
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It's easy to confuse this case with other similar cases, e.g., pulling the weights inward (speed up), or moving them outward (slow down). In those cases the angular momentum remains the same because we have a closed system, but the moment of inertia changes, hence the angular velocity must change to conserve angular momentum.
But in this case what happens is that the moment of inertia decreases (because the rotating mass decreases), but the angular momentum of the rotating student also changes (because some of the mass that was carrying that angular momentum is dropped). The net result is that there is no change in rotation speed.
The simplest way to thing about this is to imagine what happens at the instant the weights are dropped. They merely leave the student's hands and drop downward, but there are no tangential forces exerted on the student in the process, and hence no change in his/her speed of rotation.
But in this case what happens is that the moment of inertia decreases (because the rotating mass decreases), but the angular momentum of the rotating student also changes (because some of the mass that was carrying that angular momentum is dropped). The net result is that there is no change in rotation speed.
The simplest way to thing about this is to imagine what happens at the instant the weights are dropped. They merely leave the student's hands and drop downward, but there are no tangential forces exerted on the student in the process, and hence no change in his/her speed of rotation.