Does the centripetal force do work in circular motion?
Short answer: Tension is always perpendicular to velocity, so it does no work. Speed stays constant.
The trap
The wrong idea
“The centripetal force does work in uniform circular motion.”
It sounds reasonable, and a lot of JEE/NEET aspirants carry it into the exam. Here's a one-question check, then the explanation that makes it click.
Quick check
Try it before you peek
Work done by tension on a stone in uniform circular motion over one turn is:
- 2πrT
- Zero
- Depends on speed
Show the answer
B. Zero
Tension is always perpendicular to velocity, so it does no work. Speed stays constant.
The click
Work needs a component of force along the displacement: for a small step, dW = F ds cos θ. In circular motion the velocity, and so each small displacement ds, is along the tangent to the circle, while the centripetal force (here the string's tension) points along the radius toward the centre. A radius and a tangent are always at 90°, so cos θ = 0 at every instant.
Since the work over each small step is zero, the total over one turn, or any part of a turn, is zero. The tempting answer 2πrT multiplies the force by the path length and ignores the angle between them.
The work–energy theorem agrees: in uniform circular motion the speed is constant, so the kinetic energy doesn't change, and the net work must be zero. The tension changes the direction of the velocity, never its size.
This is a general result: any force that stays perpendicular to the velocity does no work. The magnetic force on a moving charge, F = q(v × B), is the classic example, which is why a magnetic field alone can't change a charged particle's speed. A caution for vertical circles: there gravity has a component along the path and does do work, so the speed changes, but the tension, still perpendicular to the motion, still does none.
Got this one? The Knot Scan finds the misconception you don't know you have, in 8 questions.