Question

1. When a particle rotates in a circle, a central force acts on it directed towards the centre of rotation. Why does this force does no work on the particle?

Answer 1

Consider the particle at any point of time as in the situation given.
The force is acting towards center. This means that the direction of force is radially towards the center of the circular path.
Also, the direction in which the displacement is taking place is tangential to the path at that point.
Thus, the force acting and the displacement taking place are at 90° angle.
We also know that the Work is defined as Dot (•) product of Force and Displacement.
As the Force and the Displacement in this case are mutually perpendicular, their dot product is zero, i.e.
F•s = 0
And, hence the work done is Zero!

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