Angular Momentum: The Counter-Intuitive Conservation Law
So now comes the weirdest conservation law, that of angular momentum. To make an analog with linear momentum, one can state the law as something like this: an object in a state of rotation tends to stay in that state until acted upon by an outside torque. Intuitively, that makes sense. A top keeps spinning. The earth keeps rotating. Angular momentum even keeps earth orbiting the sun. Furthermore, angular momentum can be understood almost as a special case of linear momentum. Think of a merry-go-round. You have to hold on to a rail to stay on the merry-go-round. Otherwise, you'll fly forward to the ground. Your linear momentum is what wants to make you fly forward. By holding on, you're applying an outside force that adjusts the direction of your linear momentum and keeps you moving in a circle. Angular momentum, instantaneously, is linear momentum whose direction is being changed by the outside force (of you, holding on).
We all have an intuitive sense for this. So what's so weird about it then? The weirdness is that angular momentum, like linear momentum, is a vector, which means there is not only an amount of angular momentum but also a direction associated with it. Physicists use the "right hand rule" to determine the direction associated with angular momentum. The rule can be implemented by rotating the fingers of your right hand in the direction of the rotation and holding your thumb straight out. Your thumb points in the "direction" of the rotation. The earth rotates west-to-east, hence north is the direction of the rotation. On the merry-go-round, if it's moving counter-clockwise from above, the direction of rotation is up.
What seems only a matter of definition has bizarre results.
Consider a wheel on an axle, say a bicycle wheel on a two-foot axle a foot to each side of the wheel. If I suspend one side of the axle from a hanging string, the wheel, of course, will fall and swing until it finally comes to rest dangling directly below the string.
If, however, I spin the wheel up to several hundred RPM's and repeat the experiment, the wheel will not fall. It will begin to revolve around the string slowly and perhaps bob a bit as it revolves. Why? Conservation of angular momentum, of course.
Remember that the direction of the angular momentum is perpendicular to the plane of rotation, so when I hang the wheel up on the
Latest Articles