Irodov Problem 1.150 – Torque and Angular Momentum in Circular Motion

Problem Statement

A particle of mass m moves in a circle of radius R with angular velocity ω. Find its angular momentum about the center and about a point on the circumference.

Given Information

• Mass m, radius R, angular velocity ω

Physical Concepts & Formulas

$$L=mvR=m\omega R^2$$

Step-by-Step Solution

Step 1: Speed v = ωR.

Step 2: L about center = mvR = mωR².

Step 3: L about circumference point (distance varies): average = mωR² + 0… actually max = 2mωR², min = 0, instantaneous varies.

Worked Calculation

L_center = mωR²

Answer

$$\boxed{L_{center}=m\omega R^2}$$

Physical Interpretation

About the center (perpendicular axis), angular momentum is constant for uniform circular motion. About a rim point, it oscillates because the moment arm changes.