Torque has dimensions of energy

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Discussion Overview

The discussion centers around the dimensional relationship between torque and energy, exploring the implications of this relationship in the context of physics. Participants examine the nature of torque as a vector quantity compared to energy as a scalar, and how this affects their interpretation and application in both translational and rotational contexts.

Discussion Character

  • Conceptual clarification, Debate/contested

Main Points Raised

  • One participant observes that torque has dimensions of energy and questions its significance.
  • Another participant argues that while torque and energy share dimensional units, they are fundamentally different due to torque being a vector and energy being a scalar.
  • A participant explains that work in rotational motion is represented by torque times the angle rotated, suggesting that torque carries the dimensions of work independently.
  • It is noted that torque can be considered as having units of "Newton metres per radian," emphasizing the dimensional equivalence to work.
  • One participant agrees that torque is the rotational analogue of work done in translational motion.

Areas of Agreement / Disagreement

Participants express differing views on the implications of torque having the same dimensions as energy. While some acknowledge the dimensional similarity, others emphasize the fundamental differences between the two quantities. The discussion remains unresolved regarding the significance of this relationship.

Contextual Notes

The discussion highlights the dependence on definitions of quantities and the interpretation of dimensions in physics. There are unresolved aspects regarding the implications of treating torque and energy as dimensionally equivalent.

Viru.universe
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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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