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Conservation of angular momentum spinning wheel on a stool?
Someone is sitting on a stool with a wheel spinning in, say, the clockwise direction (the axis of rotation is vertical). The guy then turns the wheel upside down, so that it is now spinning in the counter clockwise direction, and the person himself starts rotating in the clockwise direction:
http://www.youtube.com/watch?v=eLRFsy0fOTE
I understand this is due to the conservation of angular momentum, but I was thinking:
if the guy started moving with the stool, then something must have applied a torque on him?
Motion is always caused by a force right? So where did the force that started the rotation of the guy on the stool come from?
Thanks
But the torque the guy is exerting on the spinning wheel is being used to rotate the wheel upside down, thus giving it an 'extra' angular momentum in the direction perpendicular to its axis in order for the axis itself to perform a rotation. (torque in direction of line going through guy's belly or back)
In the end the guy starts spinning about the the axis of the stool, which is in the same direction as the axis of the spinning wheel.
If his hands are subject to the same forces (and torques) that they exerted on the axis of the wheel, shouldn't he acquire the opposite torque that he gave the wheel?
Therefore falling to the floor because the torque would be in the direction perpendicular to his belly/back.
3 Answers
- Steve4PhysicsLv 77 years agoFavorite Answer
Motion is always caused by a force right?
Not quite:
Linear acceleration of an object is caused by a resultant force.
Angular acceleration of an object is caused by a resultant torque.
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When he turns the wheel upside down, he has to exert a torque on the spinning wheel. This torque is a couple (couple = pair of non-colinear, equal magnitude antiparallel forces) perpendicular to the axis of the spinning wheel.
He will feel forces on his hands as the spinning resists him turning it upside down.
From Newton's 3rd law, it follows that an equal magnitude torque is exerted by the spinning wheel on him; this gives him angular acceleration causing his change in rotation. (When the torque is zero again, he continues turning at a constant rate in accordance with Newton's 1st Law.)
- 7 years ago
energy comes from the guy's muscles and force is the reaction of the axle on the guy's hands. Let the initial angular momentum be up wards so the applied torque must have the direction downwards. This means the reaction torque must be upwards which will produce the rotation in the same direction as the wheel initially before turning it.
