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2.5 Forces and circular motion - including acceleration and centripetal force

This section was adapted, re-edited and extended from the web page including a section on Gravity and circular motion.

Velocity is a vector quantity, it has both size (the speed) and direction.

If either the speed or direction changes, you have a change in velocity - you have an acceleration!

With this in mind, imagine whirling a conker around on the end of a piece of string, the moon orbiting Earth or planets orbiting the Sun.

What velocity are we dealing with? What force are we dealing with?

When an object goes round in a circle at a constant speed its direction is continually changing.

Even though the speed is constant, because direction changes, the velocity (a vector) is continually changing.

Therefore, if the velocity is changing, you must be dealing with an acceleration, even though the speed is constant.

To maintain this accelerating circular motion, there must be a force operating to maintain the circular path.

This is called the centripetal force - it can be the tension in a string as you whirl an object around or gravity holding some large object in orbit.

The direction of acceleration is inwards, the same direction as the centripetal force, and at 90^o to the direction of motion.

(You don't have to know this, but the acceleration of an object moving at a constant speed in a circle is v²/r)

circular motion - velocity & centripetal force

To keep a body moving in a circle there must be a force directing it towards the centre.

This is called the centripetal force and produces the continuous change in direction of circular motion.

Even though the speed may be constant, the object is constantly accelerating because the direction is constantly changing via the circular path - i.e. the velocity is constantly changing (purple arrows, on the diagram).

For an object to be accelerated, it must be subjected to a force that can act on it - Newton's 1st law of motion.

Here the resultant centripetal force is acting towards the centre, so always directing the object to 'fall' towards the centre of motion (blue arrows on the diagram).

But the object is already moving, so the force causes it to change direction.

SO, the actual circular path of motion is determined by the resultant centripetal force (black arrows and circle) and the circling object keeps accelerating towards what it is orbiting.

The centripetal force stops the object from going off at a tangent in a straight line.

Swinging something round on a string.

When you swing something round on the end of a string, the tension in the string is the centripetal force.

Imagine whirling a conker round on the end of a string.

You yourself feel this force of tension as the 'pull' in the string (I've marked in a black line to represent the string).

If you could use a fast action camera to monitor the motion and the string broke, you would observe the object would fly off at the precise tangent to the circular path and in a straight line of constant velocity - the result resultant of Newton's 1st law!

Since gravity and air friction act on the object, you do have to keep on 'inputting' kinetic energy to keep it swinging round.

The centripetal force will vary with the mass of the object, the speed of the object and the radius of the path the object takes.

 

The same arguments on circular motion apply to the movements of planets around a sun, a moon around a planet and a satellite orbiting a planet. The orbits are usually elliptical, rarely a perfect circle, but the physics is the same.

In these cases, it is the force of gravitational attraction that provides the centripetal force and it acts at right angles to the direction of motion.

You should also realise that they are moving through empty space (vacuum), so there are no forces of friction to slow the object down.

This is why the planets keep going around the Sun and the moon keeps going around the Earth.

When satellites are put into orbit they are given just the right amount of horizontal velocity so that the resultant centripetal force of gravity keeps the satellite in its a circular orbit.

You can vary this horizontal velocity to position satellites at different distances above the Earth's surface.

Notes index on acceleration, deceleration, velocity/speed-time graphs

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Keywords, phrases and learning objectives for circular motion

Be able to describe and explain the forces involved in circular motion and the acceleration and centripetal force holding one object orbiting another in a gravitational field.

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Notes index on acceleration, deceleration, velocity/speed-time graphs