Delta and the Power of Change

In physics, one of the big differences between KS3 and KS4 is the idea of “change”. KS3 students are happy to talk about speed being distance divided by time but at GCSE level you need to be thinking instead about speed being a rate of change of distance.

Why is this important? Because physics calculations are almost always about changes or differences rather than absolute values.

Suppose, for example, that you are asked to calculate the kinetic energy of an object that has a mass of 2 kg and a velocity of 10 m/s. Using the usual equation (KE = ½ mv²) you’ll get 100 J but this overlooks the fact that the object is on a spinning planet, which is itself orbiting around a star at about 30 000 m/s, all of which surely adds to the object’s kinetic energy. But the object has all of those velocities even when it is “stationary” and what we’re really interested in is how much more kinetic energy the object has when it is given an additional velocity.

In other areas of physics, the idea of change is more obvious. Electricity is the best example as we have the concept of potential difference, which you might simply have called “voltage” in the past. At GCSE we need to understand that the potential difference is a measure of the energy transferred by part of a circuit. It therefore makes no sense to talk about the potential difference at a point in the circuit because, by definition, we need two points to measure a difference.

This distinction ought to make it obvious how to use a voltmeter: connect it across the part of the circuit being measured. If you have mistakenly put a voltmeter inside a circuit, where it breaks the circuit at one point, then you probably haven’t really grasped the idea of potential difference.

So powerful is the idea of changes and differences that we use a special symbol in these situations. That symbol is the Greek letter delta, which is the “triangle” you met in the equation for gravitational potential energy.

ΔGPE = mgΔh

The delta symbol tells you that the change in GPE depends on the change in height. In other words, the amount of GPE that can be lost by an object depends on how far the object can fall. This is not an absolute measurement of height, such as height above sea level – unless, of course, the object can fall all the way down to the sea (and even then it will continue to lose GPE as it sinks to the seabed).

Whether you are moving forwards through the GCSE Physics course or you are now nearing the end of the course, try to think about processes and calculations as changes. This approach should help to give you greater insight into what is really happening and it will definitely serve you well if you continue to study physics after GCSE.