Energy, Work and Circular Motion – Learn

Work is defined as the force (F) applied to move an object some displacement (s): W=Fs. As force and displacement are vectors, we correctly say that it is only the component of the force in the direction of motion that contributes to the work being done. This now results in the equation for work becoming: W=Fs\cos { \theta }  

One of the features of circular motion, is that the centripetal force is always directed into the centre of the circle that is the path for the object. Even though the object is constantly changing direction, the motion at any instant is always tangential to the circle. This gives us the situation where the angle, \theta, between the force and the direction of motion is 90°. If we apply this to our equation for work:

W=Fs\cos { \theta }

W=Fs\cos { { 90 }^{ \circ } }

W=0

Therefore, we conclude that no work is being done on an object in uniform circular motion.

Work is also defined as the change in kinetic energy. As the work done on an object in uniform circular motion is 0, there is no change in kinetic energy for the object in uniform circular motion. Kinetic energy is given by:

KE=\cfrac { 1 }{ 2 } m{ v }^{ 2 }

The kinetic energy depends only on the magnitude of the velocity and not on its direction. In uniform circular motion, only the direction of the velocity is changing, because the force is at right angles to the movement. Since the speed (i.e. the magnitude of the velocity) is constant, no work is being done and the energy remains constant.

For an object in uniform circular motion:

  • No work is being done on the object
  • There is no change in the objects kinetic energy
  • The kinetic energy remains constant