Torque and angular momentum

A force alone does not tell you whether something will turn. Push a door in the middle of its face and it swings; push the same door just as hard right next to the hinges, or push straight along its surface towards them, and it barely moves. What matters is the force, the distance from the pivot, and the angle between them — combined in the torque, τ = rF sin θ. That sin θ is the whole reason a wrench has a long handle and you pull it sideways rather than along its length.

Angular momentum is what torque changes, exactly as ordinary force changes ordinary momentum. It is not the same quantity as linear momentum wearing a different hat: a wheel spinning in place has plenty of angular momentum and zero linear momentum, and a block sliding in a straight line is the reverse. They are separate bookkeeping, each with its own conservation law.

That conservation law is the useful part. With no net external torque, angular momentum stays fixed — so if the moment of inertia goes down, the angular velocity must go up to compensate. This is the spinning skater pulling her arms in, and nothing is being created when she speeds up: she changes only how her mass is distributed, and the product of inertia and spin rate holds. The same bookkeeping keeps a planet's orbit sweeping equal areas in equal times, and keeps a falling cat's total angular momentum at zero while it turns itself the right way up.