Centripetal Force (OCR A Level Physics)

Net Force on an Object in a Circular Path

• For an object moving in a circle, it will have the following properties:

  • Period

  • Frequency

  • Angular displacement

  • Angular velocity

• These properties can be inferred from the properties of objects moving in a straight line combined with the geometry of a circle

Motion in a Straight Line

• When an object moves in a straight line at a constant speed its motion can be described as follows:

  • The object moves at a constant velocity, v

  • Constant velocity means zero acceleration, a

  • Newton's First Law of motion says the object will continue to travel in a straight line at a constant speed unless acted on by another force

  • Newton's Second Law of motion says for zero acceleration that there is no net or resultant force

• For example, an ice hockey puck moving across a flat frictionless ice rink

Motion in a Circle

• If one end of a string was attached to the puck, and the other attached to a fixed point, it would no longer travel in a straight line, it would begin to travel in a circle

• The motion of the puck can now be described as follows:

  • As the puck moves it stretches the string a little to a length r

  • The stretched string applies a force to the puck pulling it so that it moves in a circle of radius r around the fixed point

• The force acts at 90° to the velocity so there is no force component in the direction of velocity

  • As a result, the magnitude of the velocity is constant

  • However, the direction of the velocity changes

  • This means there is acceleration present in the circular motion, so there must be a net force 

• As it starts to move in a circle the tension of the string:

  • Continues to pull the puck at 90° to the linear velocity

  • Acts towards the centre of the circle

  • Is the only force acting on the puck

  • Hence, the net or overall force is towards the centre of the circle 

• So, the net force acting on the puck is called the centripetal force

Centripetal force and acceleration are always directed towards the centre of the circle

• 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

Centripetal Force

• 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)