Understanding the Formula of Power: Torque x Angular Velocity Explained

[chetzread]

Homework Statement

i was told that Power = torque x (angular velocity)

Homework Equations

The Attempt at a Solution

I found that power has unit of Nm/s,
torque x (angular velocity) has unit of Nm(rad/s), is the formula given wrong?

 

[haruspex]

Homework Statement

i was told that Power = torque x (angular velocity)

Homework Equations

The Attempt at a Solution

I found that power has unit of Nm/s,
torque x (angular velocity) has unit of Nm(rad/s), is the formula given wrong?

Angles do not have a dimension in the way that mass, time, etc. do.
Consider e.g. that a circular arc of radius r and angle θ has length rθ.
Nevertheless, they do have units, and the unit "radian" is chosen in such a way that you do not need to include a constant in the rθ formula. It turns out that this also means you do not need a constant in the power formula if radians are used in the angular velocity.

 

[rude man]

Or, angles are dimensionless.