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
ac = v2/r

Proof: Khan Academy

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 acceleration calculator
From About Science

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 Physics 9702 Doubts | Help Page 86 | Physics Reference
Tension Load swung on a string Effects of gravity
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!

Helpful Links:

⇐ Previous in Physics: Kinematics of Uniform Circular Motion
⇒ Next in Physics: Gravitational Fields

One thought on “PHY C7: Centripetal Acceleration & Force

  1. Pingback: PHY C22: Charged Particles in Magnetic Fields – ProDuckThieves

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