# Centripetal Acceleration & Force

Show/Hide Sub-topics (Circular Motion | A Level)

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:

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

$F = mr \omega^{2}$