Torque has dimensions of energy

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SUMMARY

Torque is fundamentally different from energy, despite sharing similar units. Torque is a vector quantity, while energy is a scalar. In rotational mechanics, work is defined as torque multiplied by the angle in radians, which are dimensionless. Therefore, the SI dimensions of torque can be expressed as "Newton metres per radian," indicating that torque and work share the same units, highlighting their relationship in rotational dynamics.

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  • Understanding of vector and scalar quantities
  • Familiarity with rotational mechanics concepts
  • Knowledge of SI units and dimensional analysis
  • Basic principles of work and energy in physics
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I just noticed that torque has dimensions of energy! What does that mean?
 
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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".
 
It means torque also has the same units as work. It is the rotational analogue of work done in a translational manner.
 
Thanks a lot..
 

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