Understanding Work
* Work is done when a force causes a displacement in the direction of the force. In other words, work is the energy transferred to or from an object by the application of a force along a displacement.
* Work is calculated as: *Work (W) = Force (F) * Displacement (d) * cos(θ)*, where θ is the angle between the force and displacement.
Circular Motion
* Centripetal Force: In uniform circular motion, the force acting on the particle is always directed towards the center of the circle (centripetal force).
* Displacement: The particle's displacement in each instant is tangential to the circle.
Why Work is Zero
* Perpendicular Force and Displacement: The centripetal force acting on the particle is always perpendicular to the particle's displacement. This means the angle between the force and displacement is 90 degrees.
* Cosine of 90 Degrees: The cosine of 90 degrees is zero (cos 90° = 0).
Therefore, because the angle between the force and displacement is 90 degrees, the work done by the centripetal force on a particle in uniform circular motion is always zero.
Key Point: The particle does have kinetic energy due to its motion, but the *work done by the centripetal force* itself is zero.
