Question

The work done by a force is the product of force and distance. The torque due to a force is the product of force and distance. Does this mean that torque and work are equivalent? Explain.

Short answer

No, they are not equivalent.

Step-by-step solution

Work done and torque

We know that,The work done by a force is the product of force and distance.

$\mathit{W}\mathbf{=}\overrightarrow{\mathbf{F}}\mathbf{.}\overrightarrow{\mathbf{d}}$

WhereW is work done,F is force and is distance.

Also we know that,The torque due to a force is the product of force and distance.

$\overrightarrow{\mathbf{t}}\mathbf{=}\overrightarrow{\mathbf{r}}\mathbf{\times }\overrightarrow{\mathbf{F}}$

Where$\overrightarrow{\mathbf{t}}$ is torque,$\overrightarrow{\mathbf{F}}$ is force and$\overrightarrow{\mathbf{r}}$ is position vector.