We just discussed the rotation of a rigid body. We defined the basic concepts and used them to solve simple problems. It was kind of a similar philosophy to what we did doing kinematics a few chapters ago. But now it's time to forge ahead and try to understand better how physical laws allow you to figure out the motion of rotating bodies. This is analagous to using Newton's laws to find the motion of blocks and things like that in response to gravity and friction. But now we will include rotation motion also. For example, instead of a block sliding down a plane, we could try to figure out how fast a log rolls down a hill.
Let's summarize what we've got so far. We have quantities analogous to linear motion, angle is like distance, angular velocity is like velocity, angular acceleration is like acceleration, moment of inertia is like mass.
If we want to understand mechanics better, what else can we crib from what we've done before? Well how about momentum? We'll see there's something analogous to that called angular momentum. How about force? Yes we're lucky again, there's something called torque that behaves in a similar way. But one thing a bit odd. The above linear quantities, velocity, momentum, and force, are all vectors, yet so far we haven't talked about how to ``vectorize" the corresponding angular concept. Let's see how to do that.