6.1.5 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 force towards the centre of the circle required to keep a body in uniform circular motion. It is always directed towards the centre of the body's rotation.

•  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

Step 1: Draw the forces on the bucket at the top

Step 2: Calculate the centripetal force

• • The weight of the bucket = mg
  • This is equal to the centripetal force since it is directed towards the centre of the circle

Step 3: Rearrange for velocity v

• • m cancels from both sides

Step 4: Substitute in values