What real-world examples show not work being done? Can you think of examples other than resisting the force of gravity?

Work is defined as a force doing a movement, for example, if with a force F we move an object a distance D, the work done is:

W = F*D

(note, the force is causing the movement, the product here is a dot product, this means that if the force and the displacement are perpendiculars, the product is zero)

So the examples where there are not work being done may be:

We do not have any movement:

For example, you can go to a wall in your house and push it really hard.

There is a force, but the wall will not move, so we have D = 0

and W = F*D = F*0 = 0

Because we have no motion.

Another case is where the force and the direction of motion are perpendiculars.

If we have for example a car, moving at a constant speed, and you push it sidewise (perpendicular to the direction of movement) we have a force being applied and movement, but those are in different directions (so the force does not cause the movement) so we dont have work being done.

the tires are rotating at 0.434 rpmlinear speed=45 m/sdiameter=0.550 mradius=0.275 mnow v= rωω= v/rω=45/0.275ω=163.6 rad/sω=163.6 rad/s (1rev/2π rad) (60s/1m)ω=1563 rpm