When an object is in uniform circular motion is any work
being done to it, if it is in a frictionless environment?
The answer is no.
Seeing as the formula for determining work is…
Work = Force * Displacement * cos(θ)
The cosine of theta in
this case would end up being 90 and computing cos(90) yields 0 so the entire equation will equal 0 joules. Using other principles of physics you will know that when no work is being done on a system the total mechanical
energy (PE+KE) will not change and along with that the KE will not change so an object will continue to stay at a constant
speed as long as long as no external force is added (this perfectly shows Newton’s first law of motion). This is also the reason why the planets can orbit the sun at a constant speed.