# Centripetal Force(OCR A Level Physics)

Author

Katie M

Expertise

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

#### Exam Tip

The term centripetal force should not be confused with "centrifugal force" as this is something that is thought to act away from the centre of a circle - this is the opposite of what is happening in circular motion

## 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)

#### Worked example

A bucket of mass 8.0 kg is filled with water is attached to a string of length 0.5 m. What is the minimum speed the bucket must have at the top of the circle so no water spills out?

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

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