3.6.1.1
Centripetal force is the resultant force towards the centre
Circular Motion — AQA A-Level Physics
Key Definition
Centripetal force — The resultant force directed towards the centre of the circle required to keep a body in uniform circular motion.
$$\begin{aligned}
F &= \frac{mv^2}{r} \\
&= m\omega^2 r
\end{aligned}$$
$$\begin{aligned}
F &= \frac{mv^2}{r} \\
&= mr\omega^2 \\
&= mv\omega
\end{aligned}$$
- $F$: 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. (N)
- $m$: mass (kg)
- $v$: linear speed (m \(s^{-1}\))
- $r$: radius of orbit (m)
- $\omega$: angular speed (rad \(s^{-1}\))
- 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. is not a separate type of force. It is always provided by a real force.
- Ball on a string: tension provides the 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..
- Car on a roundabout: friction between tyres and road.
- Planet orbiting a star: gravitational force.
- Centripetal force and centripetal 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.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. directed towards the centre of the circular path, required to maintain circular motion. act in the same direction (Newton's second lawThe resultant force on an object is equal to its rate of change of momentum. For constant mass, F = ma.).
Common Mistake
MEDIUM
Students often: Listing 'centripetal force' as a separate force on a free-body diagram.
Instead: Centripetal force is the name we give to the resultant force when it acts towards the centre. It is always provided by a real force (tension, friction, gravity, etc.). Never draw it as an additional force.
Instead: Centripetal force is the name we give to the resultant force when it acts towards the centre. It is always provided by a real force (tension, friction, gravity, etc.). Never draw it as an additional force.