Question

An object with mass m moving in a circle of radius r with speed v has linear momentum of magnitude mv and an angular momentum of magnitude mvr. Is it dimensionally possible to add the magnitudes of linear momentum and angular momentum?

a).Yes, since both quantities have the same dimensions.
b).No, since the quantities have different dimensions.
c).Yes, since both quantities include mass.

Answer 1

Answer: b)

Explanation: L has units of Kg.m^2/s

P has units of Kg . m /s

However these vectors are in different plane, L is perpendicular to the plane form by the velocity and position vector from the center of the circle.