Angular Momentum: The Counter-Intuitive Conservation Law
the string the direction of the angular momentum is outward from the string (if the wheel is spinning clockwise from the perspective of the string; inward, otherwise.) Imagine that if you're watching this whole thing and the wheel is directly to the left of the string, then the angular momentum of the wheel is also to the left.
Now, gravity exerts a torque on the wheel, trying to pull it downward from the point of suspension. But consider the direction of that torque. The torque due to gravity is pulling in a direction that you see as counter-clockwise, but the true direction, by the right-hand rule, is toward you. So, we have a large amount of angular momentum pointed to the left, and a torque pointed at you. Torque, is, by definition, change in angular momentum (just as force is change in linear momentum). So, the torque changes the angular momentum by making it point more toward you, moving the angular momentum vector around from left to toward you, causing a revolution of the wheel about the string. As the wheel revolves, the torque vector is always perpendicular to the angular momentum vector, and the wheel just keeps revolving, but does not fall.
Of course, as friction takes its toll the wheel's spin slows, and the wheel slowly starts to fall under the relentless force of gravity.
Now, why is this important to astronomers? Next time, I'll discuss some of the strange yet crucial effects angular momentum has in astrophysical systems.
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