# PHY C7: Centripetal Acceleration & Force

Today we’ll be covering:

• Centripetal Force
• Centripetal Acceleration
• Equations

Let’s jump in!

What is Centripetal Acceleration?
Acceleration towards the centre of a circle.

When an object is in circular motion, it constantly changes its velocity.
Although the speed is constant, the direction of motion changes, so the velocity must also change.
A change in velocity is an acceleration.
We can find the change in velocity using vector subtraction.

In this diagram, consider the vectors v1 & v2.
Red arrow between v1 & v2 = Δv = v2 – v1

You can see that the object’s acceleration is PERPENDICULAR to the direction of motion.
It acts TOWARDS the CENTRE of the circular path.
Hence, the acceleration is centripetal: towards the centre.

As a formula:
ac = ω2r
OR
ac = v2/r

What is Centripetal Force?
Force acting towards the centre of a circle.

Since F = ma, the centripetal acceleration must be caused by a force.

Centripetal force (Fc) acts in the SAME direction as the centripetal acceleration.
It acts PERPENDICULAR to the direction of motion of an object in circular motion.

We can get 2 equations from
Fc = mac :

Fc = mω2r
Fc = mv2/r

As with every force, this force must be PROVIDED by a source.
A few Providers of Centripetal Force:

 Provider Situation Image Gravitational force Planets & satellites in orbit Tension Load swung on a string Friction A car turning around a corner From Brilliant

In all these situations, you can see that the forces act toward the centre of the circular path!