AQA Physics A-level Year 2
Essential Notes Note that the force is centripetal (towards the centre), NOT ‘centrifugal’(away from the centre). People talk about centrifugal force ‘throwing’ them off their feet as a bus takes a sharp corner, or being responsible for spin-drying clothes. Using centrifugal force to explain these phenomena is a good way to make your teacher apoplectic. The person on the bus, or the water drops in a drier, are simply obeying Newton’s First Law; i.e. continuing to move in a straight line, until acted on by a force.
Centripetal force Since an object moving in a circle is accelerating there must be a resultant force acting on it. The resultant force could come from gravity, as in the case of a satellite orbiting the Earth, or from the tension in a string, as in the case of a conker being whirled round. The resultant force is centripetal; it acts towards the centre of the circle. The size of the centripetal force that is needed to keep a mass, m, moving in a circle with a radius, r, at a velocity v, is given by Newton’s Second Law in the form F 5 ma. The centripetal acceleration is v2/r, so the centripetal force has to be F
mv 2 mr ω 2 r
Centripetal force: • increases with mass, so that a larger force is needed to make a larger mass move at the same speed in a circle; • increases with the square of the speed; this means that it takes four times as much friction to keep a car on the road if you take a corner twice as fast; • decreases as the radius increases, so the force increases if the circle gets smaller. (a)
satellite
Notes It is a common mistake in circular motion problems to invent an extra force called the centripetal force. Remember that this is not an extra force but simply the resultant of the real forces acting on the object in circular motion. Stick to real forces, with real causes.
F
(b)
lift × sinθ
lift
(c) R
lift × cos θ
θ
θ
weight
Fig 5 Examples of circular motion
For a satellite, it is gravity that provides the centripetal force
Earth
For an aircraft that is turning (banking), it is a component of the lift that provides the centripetal force
R cos θ
For a cyclist on a banked track, it is a component of the reaction force that leads to a centripetal force
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