Angular momentum is the product of which quantities?

• A. Mass times velocity
• B. Displacement times force
• C. Angular momentum is the product of the moment of inertia and angular velocity
• D. Radius times density

Answer: (C)

Angular momentum describes rotational motion, and for an object spinning about an axis it equals the product of how mass is distributed relative to that axis and how fast the rotation is (the angular velocity). In symbols, L = I ω. The moment of inertia I depends on mass and its distance from the axis—the more mass farther from the axis, the larger I becomes, so the same spin speed yields a larger angular momentum. The angular velocity ω tells you how quickly the rotation occurs, so increasing ω increases L as well.

For a single particle moving in a circle, this idea still holds: L = m r^2 ω, which matches L = I ω if you treat the particle’s I as m r^2. This comes from the relationship L = r × p, and with p = m v and v = ω r (perpendicular to r), you get |L| = m r v = m r^2 ω.

So angular momentum is not mass times velocity (that’s linear momentum), nor a product of displacement and force, nor a simple radius times density. It’s the rotational counterpart where distribution of mass and rotation rate determine the amount of angular momentum.