Subject knowledge and
 challenging concepts

• Circular motion is the result of two forces: one, centripetal force, is towards the centre of the circle; the other, tangential force, is provided by the means of propulsion of the mass. The centripetal force is greater if the mass is greater and if the speed is greater, but becomes less if the radius is greater. The formula linking the centripetal force with the mass of the object in circular motion, its velocity and the radius of the orbit is F = mv²/r.
• If a mass were attached to a string and caused to orbit a person, it would describe a circular path. If the string were to snap, the flight path of the mass would be a straight line at a tangent to the circle. It would not be a line radial to the circle.
• Circular motion is a problematical concept because, in common with a number of forces topics at this level, it is counterintuitive. Someone experiencing circular motion, such as driving round a roundabout or riding on a fairground roundabout, can feel themselves being forced outwards and so they will want to explain this with terms such as centrifugal force. This is a misconception, but like all misconceptions it is best dealt with by having a climate for learning in which students feel safe to express ideas and feel that they won�t be �thought less of� for holding such ideas. Establishing what students really think is a strong teaching approach; subsequent challenges, activities and inputs can then be focused on. Centripetal force pulls an object in circular motion towards the centre of the circle and has to be present. Centrifugal force is an illusion caused by the perception that such an object is attempting to move in a radial direction.
• Gravity is a universal force of attraction between any two masses, and is greater if those masses are greater and is less if the distance between them is greater. This attraction is part of the reason why objects, such as the Earth and Moon, orbit each other. They are accelerating towards each other but also have a tangential motion, the result being motion in orbits. Planets in the solar system have orbits that are elliptical, with the Sun at one focus. The further a planet is from the Sun, the greater its period of orbit.
• A useful thought experiment to summarise this is credited to Newton. Imagine standing on top of a hill and firing a cannon. The ball flies out and falls to Earth. Fire subsequent cannon balls with progressively greater force so that they travel further before landing. Eventually one would travel with such force that it would be in Earth�s orbit. A greater force still would enable it to move away from the Earth.
• When an artificial satellite is put into orbit there is a precise connection between the height of the satellite above the Earth and the correct speed to keep it in orbit. The greater the height, the less the speed to keep it in orbit. This means that a low orbiting satellite has a relatively high speed, taking only an hour or so to orbit the Earth. Such satellites are useful for applications such as imaging of land and weather systems.
• There is one particular height at which the speed means that the satellite is orbiting the Earth once every 24 hours. If it is arranged that this is in the same direction that the Earth is rotating then, relative to a fixed point on the Earth, the satellite appears to be stationary. This is known as geostationary or geosynchronous. Such satellites are particularly useful when it comes to telecommunications as they provide a continuous link, and weather images from these satellites will cover a larger area than the polar orbiting ones.
• A comet has an orbit that is often highly elliptical; as it approaches the Sun its speed increases, and as it heads off further out again, the speed decreases.

Figure 1. A 'thought experiment' of Newton's