M5S8: Torque & Work Done in Circular Motion

Investigate the relationship between the total energy and work done on an object executing uniform circular motion:
 `W=F_c*s*costheta`
Work done during uniform circular motion
During uniform circular motion, the speed of an object does not change which means its kinetic energy remains constant.
`KE=1/2mv^2`
This also means no work is done on the object as otherwise it would accelerate while gaining kinetic energy.
While centripetal force acts on an object throughout uniform circular motion, it is not in the direction of its displacement so we cannot apply the formula `W=Fd` in this scenario.
The relationship between force and work done can be more accurately characterised by the following equation:
`W=F_c*s*costheta`
`theta` is the angle between direction of force and direction of displacement s of an object in circular motion.
In uniform circular motion, the net force (centripetal force) is acting orthogonal (90 degrees) to the object's direction of movement. This means `costheta` is always `cos90º` which equals zero.
Therefore, work done during uniform circular motion is zero.
You can read about and revise circular motion here.
Practice Question 1 (HSC 2004)
A car with a mass of 800 kg travels at a constant speed of 7.5 m s−1 on a roundabout so that it follows a circular path with a radius of 16 m.
A person observing this situation makes the following statement.
‘There is no net force acting on the car because the speed is constant and the friction between the tyres and the road balances the centripetal force acting on the car.’
Assess this statement. Support your answer with an analysis of the horizontal forces acting on the car, using the numerical data provided above.

Investigate the relationship between the rotation of mechanical systems and the applied torque:
Torque
r is the radius of circular motion or distance between the pivot and point of force contact. `theta` is the angle between the lever vector and applied force F that is causing the rotation/circular motion.