Centripetal acceleration
Circular Motion - OCR A-Level Physics
Key Definition
Centripetal acceleration
The acceleration directed towards the centre of the circular path that causes the change in direction of velocity for an object in circular motion.
The acceleration directed towards the centre of the circular path that causes the change in direction of velocity for an object in circular motion.
$$\begin{aligned}
a &= \frac{v^{2}}{r} \\
&= \omega^2 r
\end{aligned}$$
$$\begin{aligned}
a &= \frac{v^{2}}{r} \\
&= r\omega^2
\end{aligned}$$
- Even though the speed is constant in uniform circular motion, the velocity is changing because its direction changes continuously.
- A changing velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹. means there must be an accelerationThe rate of change of velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹.. A vector quantity. Measured in m s⁻²., and by Newton's second lawThe resultant force on an object is equal to its rate of change of momentum. For constant mass, F = ma., a resultant force.
- The accelerationThe rate of change of velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹.. A vector quantity. Measured in m s⁻². is always directed towards the centre of the circular path (centripetal means 'centre-seeking').
- The accelerationThe rate of change of velocity. A vector quantity. Measured in m s⁻². is perpendicular to the velocity at all times, which is why it changes direction but not speed.
Common Mistake
MEDIUM
Wrong: Saying there is a centripetal forceThe resultant force directed towards the centre of a circular path that causes an object to move in a circle. It is not a separate force but the net force providing circular motion. AND a centrifugal force acting on the object.
Right: There is only a centripetal forceThe resultant force directed towards the centre of a circular path that causes an object to move in a circle. It is not a separate force but the net force providing circular motion. (directed inward). 'Centrifugal force' is a fictitious force that only appears in a rotating reference frame. In the exam, always describe the real inward force.
Right: There is only a centripetal forceThe resultant force directed towards the centre of a circular path that causes an object to move in a circle. It is not a separate force but the net force providing circular motion. (directed inward). 'Centrifugal force' is a fictitious force that only appears in a rotating reference frame. In the exam, always describe the real inward force.