3.3.2: The Direction of Angular Momentum
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Just like momentum (sometimes called “linear momentum” when you want to be clear that you’re not talking about angular momentum), angular momentum is a 3-vector. With regular momentum, it’s pretty easy to figure out what the direction of the 3-vector is: it’s the direction that the object is moving. What, however, is the direction of angular momentum? If an object is spinning, it assuredly has angular momentum. However, the bits of the object are all moving in different directions (the bits on one side of a rotating disk are moving in the opposite direction from the bits on the far side), and what’s more, later any given bit of the object will be moving in a different direction.
It turns out there is a unique direction for rotation: the axis about which an object is rotating. As such, we can define the direction of the angular momentum 3-vector to be pointing along the axis of rotation. If a Frisbee is flying through the air, rotating, and is parallel to the ground, you would say that its angular momentum 3-vector points either up or down.
How do you figure out up or down? This is just a matter of convention. The convention we use is called the right-hand rule. What you do is curl the fingers of your right hand so that they point around in the direction of the rotation. Stick your thumb straight out, and it points along the direction of the angular momentum 3- vector. For example, if you’re looking down on a Frisbee, and the Frisbee is rotating counter-clockwise, you would say that it’s angular momentum 3-vector is pointing straight up. (Try using your right hand to see why that would be the case.)