# Torque has dimensions of energy

1. May 7, 2013

### Viru.universe

I just noticed that torque has dimensions of energy! What does that mean?

2. May 7, 2013

### VantagePoint72

It doesn't really mean anything. Energy is a scalar and torque is a vector, so they are fundamentally different quantities. In the same way that, for translational energy, work is the force (or, rather, the component of force in the direction of motion) times distance moved, for rotational energy work is the torque times the angle rotated through. We conventionally measure angles in radians, which are dimensionless since they are ratios of distances. Thus, torque must carry all the dimensions of work by itself. If you like, you can consider the SI dimensions of torque to "really" be "newton metres per radian". It's the same idea as angular frequency which mathematically has units of "1/seconds" but really represents the dimensionally equivalent units of "radians per second".

3. May 7, 2013

### SteamKing

Staff Emeritus
It means torque also has the same units as work. It is the rotational analogue of work done in a translational manner.

4. May 11, 2013

### Viru.universe

Thanks a lot..