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Forces 2: 2.3 Gravity, velocity, centripetal force and circular motion

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INDEX of physics notes on FORCES section 2 on mass, weight and gravity

2.3 Forces: Gravity, velocity, centripetal force 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 (right of diagram below).

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

Diagram illustrating circular motion - velocity and 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.

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

You yourself feel this force of tension as the 'pull' in 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.

For more on motion and acceleration see Acceleration, velocity-time graph interpretation and calculations, problem solving

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.

For more on motion and acceleration see

Acceleration, velocity-time graph interpretation and calculations, problem solving

INDEX physics notes FORCES section 2 on mass, weight and gravity

Keywords, phrases and learning objectives for forces

Be able to explain how the forces of gravity keeps objects orbiting around each other e.g. moons around a planet, planets orbiting a star like our sun forming the solar system.

 Know in these orbit system the speed is constant but the velocity is constantly changing,

Know that the centripetal force determines the circular motion of moons, satellites and planets.


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INDEX physics notes FORCES section 2 on mass, weight and gravity