Circular Motion

Centripetal Force

According to Newton’s First Law of Motion, an object will move in the direction of the resultant force acting upon it. If an object has forward motion and a second force acts upon it, then the object will move in that direction. This is a form of acceleration.

In the case of circular motion, the object has forward motion, but there is a constant inwardly directed force making it turn. This inward resultant force is called the Centripetal Force.

In this diagram, you can see a mass (m_) with a forward velocity (tangential velocity) (_v) .

The mass experiences a force (a_c) towards the centre of the circle. This is the centripetal force.

Centripetal force can act in various ways. The tension in the chain of a swing in the park is an example of centripetal force acting through a solid object.

When a car or bike turns the centripetal force acts via the friction (grip) between the tyres and the road surface.

Gravity is a very important form of centripetal force. The gravitational pull of the sun keeps us in orbit, as does the Earth’s gravitational pull on the moon and the satellites in orbit too.

When an object is in a stable orbit the forward velocity balances the pull of gravity. This is why satellites stay in orbit, it is why we orbit the sun and don’t crash into it.

Velocity

When an object is in a circular motion it has to have forward velocity, but because it is changing direction, this velocity is constantly changing too.

Recall that velocity is a vector quantity, this means it has both magnitude and direction. Therefore, even if the magnitude, (speed) stays constant the velocity is changing due to the change in direction.

Acceleration is defined as a change in velocity over time. When an object is in a circular path it is accelerating, due to the constantly changing direction of the object’s velocity.

You may have experienced this if you have taken a corner too quickly on your bike or when in a car.

In circular motion:

• Speed can be constant.

• Velocity is changing (direction not magnitude).

• The object is accelerating (angular acceleration).

The change in velocity (acceleration) is greater if the forward velocity is higher and if the radius of the turn is smaller.

Remember this when you learn to drive, taking a tight corner at a high speed produces more acceleration.

As Force = mass x acceleration, the forces on the car and you are higher too. This makes the car harder to control.

When an aeroplane banks and turns the lift from the wings pull the plane into the turn. What is the name of this inwardly directed force?

Centripetal

What is the centripetal force that keeps Mars orbiting the sun?

Gravity