__– 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

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

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

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

__-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.

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

centripetal force:

now

So

which means

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

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