Centripetal acceleration and force
Section: Motion in a Circle | Syllabus: Cambridge A Level Physics (9702)
Uniform Circular Motion and Acceleration
In uniform circular motion, the speed v is constant, but the velocity vector is constantly changing direction.
Examiner's ReasoningAcceleration is the rate of change of velocity. Since velocity direction is changing, the object is accelerating even though its speed is constant. This acceleration always acts towards the centre (centripetal).
a = (v^2/r) or a = rω^2Units: m s^-2
Centripetal Force
According to Newton’s Second Law (F = ma), acceleration is always caused by a resultant force in the same direction.
F = (mv^2/r) or F = mrω^2 The "Centripetal" LabelCentripetal force is not a new type of force. It is simply the name we give to the net force that maintains circular motion. It must be provided by a real physical force.
| System | Physical Origin of F_c |
|---|---|
| Planet orbiting Sun | Gravitational Force |
| Car turning on flat road | Lateral Friction |
| Electron in atom | Electrostatic Attraction |
| Whirling a ball on string | Tension in the string |
Apparent Weight on a Rotating Earth
Because the Earth rotates, objects on the surface are in circular motion. The required centripetal force affects the normal contact force (N) we feel as "weight".
- At the Equator: Weight acts toward the centre, Normal force acts outward. The resultant force towards the centre is F_c = W - N.
- Therefore, N = mg - mrω^2.
- Conclusion: You feel slightly lighter at the equator because some of the gravitational pull is "used up" providing the centripetal force for your rotation.
- At the Poles: r = 0, so F_c = 0 and N = mg. You feel your full weight.
Never write about "Centrifugal Force" in an exam. It is a fictitious force. The feeling of being pushed outward is just your inertia-your body's resistance to changing its straight-line path.
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