## What to expect

In this topic we will consider another form of oscillatory motion: that of objects moving in a circle. For objects moving horizontally or in space, this is usually straightforward to model with the same force acting throughout. However, vertical circles involve changing sizes of relative forces (and often speed) due to the gravitational force. You will then consider forces that act between masses more generally, and the types of gravitational field.

After studying this topic, you should be able to:

- Perform calculations for objects moving in a circle
- State Newton's law of gravitation
- Compare uniform and radial fields
- Explain how the radius of a satellite's orbit affects its speed

And, at Higher Level:

- Describe how satellites stay in orbit even though they are not powered by anything
- Derive the relationship between gravitational potential energy and position for a non-uniform field

## Key questions

#### What is the difference between the centripetal and centrifugal force?

The centripetal force is the resultant force acting towards the centre that makes a body travel in a circle. In everyday speech, we might refer to a centrifugal force as flinging objects outward. In fact, this does not exist and instead is an effect of the absence of sufficient force while the system turns the corner. Find out more.

#### What does Newton's law of gravitation state?

Newton's law of gravitation states that every particle of mass attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to their separation squared. Find out more.

#### What is a characteristic of a uniform gravitational field?

In a uniform field, gravitational field strength is constant (9.81 N kg^{-1} on Earth) and field lines are equidistant and parallel. Find out more.

#### What is a radial gravitational field?

Beyond the distance from a mass at which fields can be assumed to be uniform, gravitational fields from point or spherical masses are radial. Gravitational force can be calculated from Newton's law. Both force and field strength are vector quantities that obey inverse-square law behaviour. Find out more.

#### What is escape speed?

A ballistic object (i.e. a particle without its own engine) can theoretically be given sufficient kinetic energy to fully escape the gravitational field of the mass on which it is situated. The escape speed is the speed that would just be enough to escape the field. To derive an expression for this escape velocity, we use conservation of energy. Find out more.

### Circular motion

We have all experienced circular motion!

### Gravitation

A field is a region of space where a force is experienced.

### AHL Gravitational fields

Close to the surface of a large mass (like Earth), the effects of gravitation are uniform. Further out, we realise the the gravitational field of a spherical mass is in fact radial. This has implications for how we calculate forces, field strength, potenti