# 6.1.5 Centripetal Force

### Calculating Centripetal Force

• An object moving in a circle is not in equilibrium, it has a resultant force acting upon it
• This is known as the centripetal force and is what keeps the object moving in a circle
• The centripetal force (F) is defined as:

The resultant perpendicular force towards the centre of the circle required to keep a body in uniform circular motion

•  Centripetal force can be calculated using:

Centripetal force is always perpendicular to the direction of travel

• Where:
• F = centripetal force (N)
• v = linear velocity (m s-1)
• ⍵ = angular speed (rad s-1)
• r = radius of the orbit (m)
• Note: centripetal force and centripetal acceleration act in the same direction
• This is due to Newton’s Second Law
• The centripetal force is not a separate force of its own
• It can be any type of force, depending on the situation, which keeps an object moving in a circular path

Examples of centripetal force

#### Worked Example

A bucket of mass 8.0 kg is filled with water is attached to a string of length 0.5 m and tension 7.0 N at the top of the circle.

What is the minimum speed the bucket must have at the top of the circle so no water spills out?

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