Why does a force not do any work if it's perpendicular to the motion?

Question

I have a book that says the Moon's orbit is [in this context assumed to be] circular. The Earth does no work on the moon. The gravitational force is perpendicular to the motion. Why is there no work done if support force is perpendicular to the motion?

Answer 1

The work done is define as follows,

W = F • d, where W= work done, F is the applied force and d = distance traveled by the object

Remember this is a dot product. That's mean W = Fd cos (θ) where θ = angle between F and d.

If θ = 90 i.e force is perpendicular to the motion, cos (90) =0 . Therefore W =0