• 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 perpendicular to the velocity, and therefore directed towards the centre of the circle, required to keep a body in uniform circular motion

• ?The magnitude of the centripetal force?F?can be calculated using:

Centripetal force is always perpendicular to the linear velocity (i.e., the direction of travel)

• Where:
  • F?= centripetal force (N)
  • v?= linear speed (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
  • For example, tension, friction, gravitational, electrical or magnetic

Examples of centripetal force

• When solving circular motion problems involving one of these forces, the equation for centripetal force can be equated to the relevant force equation
• For example, for a charged particle travelling in a circle, the?centripetal force?causing the charged particle to move in a circle is provided by the?magnetic force
• Therefore, equating the expressions for centripetal force and magnetic force gives the following:

• Where:
  • B?= magnetic field strength (T)
  • q?= charge on the particle (C)
  • m?= mass of the particle (kg)
  • v?= speed of the particle (m s?1)
  • r?= radius of orbit (m)

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