Torque and work are both equal to force time distance. How do they differ ?

Explanation

To explain the difference between torque and work, we need to analyze their definitions, mathematical representations, and physical meanings step by step.

### Step 1: Definition of Work
Work is defined as the product of force and displacement in the direction of the force. Mathematically, it is represented as:
\[ W = \mathbf{F} \cdot \Delta \mathbf{S} \]
where \( \mathbf{F} \) is the force vector and \( \Delta \mathbf{S} \) is the displacement vector. The dot product indicates that only the component of the force that acts in the direction of the displacement does work.
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