Units of Linear Speed in a Circular Motion

Question

During Uniform Circular Motion, the linear speed of the particle is defined as the radius times the angular speed. $$ v = r\omega $$ The units of linear speed is meters/second (m/s). But the units of $ r\omega $ is $ m\frac {rad}{s} $. How is this possible? And why does the unit "radian" cancel out?

Thanks for the question. I teach students circular motion right now and I'll mention it for them too. If you were confused, they also can be puzzled :) — Andrei Z., Oct 24 '21 at 09:15

score 2 · Accepted Answer · answered Oct 24 '21 at 08:59

2

Rad is a dimensionless unit. It is defined as such an angle that it intercepts an arc on a circle with the length equal to the radius of a circle. Angle in radians is the length of an arc over radius, therefore meter over meter: $\theta = L_{arc}/R$. They are dimensionless in nature and people write "rad" simply for convenience.

answered Oct 24 '21 at 08:59

Andrei Z.

330

I write radians or rad to indicate that I'm talking about an angle. – R.W. Bird Oct 24 '21 at 17:36

Units of Linear Speed in a Circular Motion

1 Answers1