# Examples of circular motion

This page contains lots of exciting examples: space men, cowboys, roller coasters, the wall of death and igloos.

The key thing to learn is the necessity of drawing all of the forces acting on the object that is moving in a circular path without drawing an extra 'centripetal force' arrow. This way you should be able to cope with horiztonal and vertical circles, whether the object is kept in motion by a tension, weight, contact force or friction.

Key Concepts

A mass on a string travels in a circle if the force exerted by the string always acts perpendicular to the direction of motion, this will happen if the other end of the string is fixed.

It´s not possible to make a vertical circle with constant velocity on the Earth because the mass is accelerated by gravity:

• At the top of the circle, weight will be adding to the tension to give the total centripetal force (Fc = mg + T)
• At the bottom of the circle, weight will be acting away from the tension (Fc = T - mg)

Essentials

Cylinder and cone

In the wall of death, a car or motorbike travels around the inside of a cylinder. A normal contact force provides the centripetal force. There must be friction to balance the weight.

Travelling inside a cone does not require upward friction; the normal force has both horizontal and vertical components.

Cyclist on an igloo

In a 'cyclist on an igloo' problem, the rider is travelling in a vertical circle but on the outside.

The centripetal force is therefore: $$mg-N={mv^2\over r}$$

Test Yourself

Use quizzes to practise application of theory.

Exam-style Questions