Analyse the forces acting on an object executing uniform circular motion in a variety of situations

– cars moving around horizontal circular bends

The only force acting on this car in the horizontal is the force of friction

Hence the frictional force towards the center of the circular path should be equal to , where m is the mass of the car , v is the velocity of the car and r is the radius of the circular path.

-a mass on a string

The circular motion is in a vertical plane.

At every point in the uniform  circular motion , the centripetal force acting on the mass must be equal to centripetal force

The tension in the string at :

  • point A is T1
  • point B is T2
  • point C is T3

At the top point A, the net force is  T1+mg. Which implies net force

At point be B, the downward force is mg, and the inward force towards the center is T2. Hence net force

At point C, the net force acting is T3 – mg. Hence net force

-objects on banked tracks

A free body diagram of the car would be as follows:

without friction, the only inward force here is Nx, a component of the Normal force on the car from the road.

normal force

Now we know normal force[since there is no motion in the y axis]

centripetal force: centripetal force

now normal force

So centripetal force

which means

road angle

to achieve speed v, without friction, the roads need to be banked at an angle road angle

Extract from Physics Stage 6 Syllabus © 2017 NSW Education Standards Authority (NESA)