Centripetal Acceleration & Force

When an object is in uniform circular motion, the angular velocity and linear velocity of the object moving in a circle is constant.

Centripetal Acceleration, a

  • centre-seeking
  • is always perpendicular to the velocity
  • always acts towards the centre of the circular motion

Useful Equations: (Memorise)

$a = \frac{v^{2}}{r}$

$a = r \omega^{2}$

$a = v \omega$

Since the centripetal acceleration is always directed towards the centre of the circular path, and the speed of the body is constant, the resultant force must also be directed towards the centre of the circle. The resultant force is centripetal force.

  • Should not be drawn in as a force in free body diagrams.
  • Does not perform any work when a particle moves in a circle because it is perpendicular to the displacement of the particle at any point in its motion.

Useful Equations:

$F = \frac{mv^{2}}{r}$

$F = mr \omega^{2}$

Mathematical Formulation

For uniform circular motion, the centripetal force ((F_c)) needed to keep an object moving in a circle with radius (r) at a speed (v) is given by (F_c = m\frac{v^2}{r}), where (m) is the mass of the object. This equation highlights the direct relationship between the force needed and the square of the speed of the object, as well as its inverse relationship with the radius of the circle.

Back To Circular Motion (A Level Physics)

Back To A Level Physics Topic List

Mini Physics

As the Administrator of Mini Physics, I possess a BSc. (Hons) in Physics. I am committed to ensuring the accuracy and quality of the content on this site. If you encounter any inaccuracies or have suggestions for enhancements, I encourage you to contact us. Your support and feedback are invaluable to us. If you appreciate the resources available on this site, kindly consider recommending Mini Physics to your friends. Together, we can foster a community passionate about Physics and continuous learning.

Leave a Comment

This site uses Akismet to reduce spam. Learn how your comment data is processed.