Arbeidsenergiestelling voor beweging langs een curve

The work done to displace an object along a curved path equals the change in the kinetic energy of the object. This is the work-energy theorem.

Consider a ball attached to a string of negligible mass, initially at rest. As the ball is dropped, it swings, tracing a circular path.

A free-body diagram can be drawn to understand the forces acting on the ball at any arbitrary point on its path.

The work done can be found by integrating the product of the force component along the displacement and the displacement.

Putting the force and the displacement as a function of angular displacement and integrating the expression from the initial to the final position, the expression of work done is obtained.

The work equals the change in kinetic energy of the ball.

As the ball is initially at rest, its initial kinetic energy is zero. So, the final kinetic energy at the lowest point is the same as the potential energy of the ball at its initial position.