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)
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.
Use quizzes to practise application of theory.
START QUIZ!
A mass moves in a circle on the end of the string in the absence of gravity. The string is held by a spaceman.
Which statement is true?
There is only one force and that is tension. This provides the force needed to hold the mass in a circle.
A ball on the end of a string moves in a horizontal circle as shown.
The centripetal force is provided by:
Horizontal component of tension acts towards the centre.
A ball travels around the inside of a cone as shown.
Two forces act on the ball, normal force N and weight W.
The centripetal force is:
Horizontal comp of N. If the cone gets steeper the angle gets smaller and so will the horizontal component. This means it must be related to cosθ
A mass moves in a vertical circle on the end of a string on Earth. At one moment of time it is in the position shown:
The centripetal force is:
This is a tricky one. The ball is accelerating down as well as towards the centre so the resultant force is not towards the centre
A roller coaster ride is built so that the riders have a feeling of weightlessness at the top of the loop.
At which point will the car need to be released for this to happen (ignore air resistance and friction)
Feeling weightless means in free fall so normal force = 0 but must have enough speed to complete the loop.
C is about 2.5 x radius
don't really need to know that A and B are too small for car to have velocity at the top and D is higher than necessary.
A ball travels around a vertical cylinder as shown.
The ball slows down due to air resistance, which of the following statements explains what happens
It is possible but there must be friction. The normal force is related to the speed so when it slows down N gets less. The friction = μN so will also get less until it is less than W.
How much of Examples of circular motion have you understood?
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