Irodov Problem 1.211

Problem Statement

Find the angular momentum of a particle of mass m moving along a circular path of radius R with speed v, about the center of the circle.

Given

m, v, R. Uniform circular motion.

Concepts & Formulas

L = m·v·R (for circular motion, r ⊥ v at all times, so sinθ = 1).

Step-by-Step Solution

Step 1: L = |r × p| = m|r × v|.
Step 2: r = R, v perpendicular to r → L = mRv.
Step 3: Direction: perpendicular to the plane of the circle (by right-hand rule).

Worked Calculation

L = mRv.

Boxed Answer

L = mRv

Physical Interpretation

Angular momentum is conserved if no torque acts. For uniform circular motion on a smooth track, L = mRv remains constant throughout.