6.1.2

# Circular Motion 2

Test yourself

## Centripetal Acceleration

Acceleration is a change in the direction or magnitude of the velocity. In a circle, the velocity is always changing. This means that the object is always accelerating.

### Change in velocity

• We can use vectors to find the change in velocity of an object between two points.
• If we make a triangle of vectors with the initial and final velocity we see that the change in velocity is always pointing towards the centre.
• In circular motion, the acceleration always points towards the centre of the circle.

### Centripetal acceleration

• The acceleration in circular motion is always directed towards the centre of the circle, this is because the change in velocity is directed towards the centre.
• Acceleration = change in velocity ÷ change in time
• $a{_c}={\Delta}v\;{\div}\;{\Delta}t$
• This is called centripetal acceleration.

### Calculating acceleration

• Centripetal acceleration can be found using linear or angular quantities:
• $a{_c}={\Delta}v\;{\div}\;{\Delta}t$
• $a{_c}=v^2 {\div} r$
• $a{_c}=r{\omega}^2$

## Centripetal Force

Any force which causes circular motion is known as a centripetal force. The larger the centripetal force, the smaller the circle.

### Forces towards the centre

• The direction of centripetal force is always towards the centre of the circle.
• Any combination of forces can cause a centripetal force, for example, the earth's gravity on the moon.
• Centripetal force is always perpendicular to the instantaneous velocity.

### Calculating centripetal force

• According to Newton's second law of motion, the net force is mass times acceleration.
• $F{_c}=ma{_c}$
• By substituting in the equation $a{_c}=v^2/r$
• $F{_c}=mv^2/r$
• Where m is the mass of the object.