The angular momentum L for a point mass is given by which expression?

The angular momentum L for a point mass is given by which expression?

• A. L = m r
• B. L = m v / r
• C. L = r m v
• D. L = m r^2 omega

Answer: (C)

The quantity that measures how much rotation a mass has about a point comes from L = r × p, with p = m v. Its magnitude is L = m r v sin(theta), where theta is the angle between the radius vector and the velocity. When the motion is circular, the velocity is perpendicular to the radius, so sin(theta) = 1 and L = m r v. That directly ties angular momentum to the radius and the tangential speed. If you want to express it in terms of angular velocity, for circular motion v = r omega, so L = m r v becomes L = m r^2 omega. Both forms are consistent for circular motion, but the simplest expression in terms of linear speed is L = m r v, which is why that option is chosen. The other forms don’t generally give angular momentum: L = m r lacks velocity entirely, and L = m v / r has the wrong units. The last form is only equivalent when v = r omega, i.e., for circular motion; without that condition, it isn’t the correct general expression.

The quantity that measures how much rotation a mass has about a point comes from L = r × p, with p = m v. Its magnitude is L = m r v sin(theta), where theta is the angle between the radius vector and the velocity. When the motion is circular, the velocity is perpendicular to the radius, so sin(theta) = 1 and L = m r v. That directly ties angular momentum to the radius and the tangential speed.

If you want to express it in terms of angular velocity, for circular motion v = r omega, so L = m r v becomes L = m r^2 omega. Both forms are consistent for circular motion, but the simplest expression in terms of linear speed is L = m r v, which is why that option is chosen. The other forms don’t generally give angular momentum: L = m r lacks velocity entirely, and L = m v / r has the wrong units. The last form is only equivalent when v = r omega, i.e., for circular motion; without that condition, it isn’t the correct general expression.