STEP Mechanics - What Do You Need to Know?

Age 16 to 18
Challenge Level
I have met many students who are rather confident at tackling Pure Mathematics on STEP, but who will not even look at the Mechanics (or Statistics) questions. In this article, I will share some of the ideas you should consider before ruling out Mechanics as an option for you.

The main hurdle to overcome when trying a Mechanics STEP question is one of mathematical modelling. The mathematics required to solve the problem is in some cases more straightforward than you would expect on a STEP question, but there is quite a bit of work to be done to get to the stage of having recognisable mathematics problems to be solved. You are given a situation, and you are required to interpret it and then work out which principles of mechanics apply, so that you can construct the necessary equations. But the good news is, once you've worked out your model, you've done most of the hard work!

Anyone who has been working through the STEP Prep resources and reading each article carefully will know what's coming next - draw a diagram! Almost every mechanics question is made more tractable by taking the information you are given and drawing a big, clear diagram with all relevant information included. One top tip a friend gave me was to have different coloured pens or pencils, so that you can mark forces in one colour and velocities in another. Another top tip is to use dotted lines to show components of vectors if you are resolving in two perpendicular directions. For collisions, it can be useful to draw a "before" and "after" diagram so that you can be clear about forces acting and velocities immediately before and after a collision.

Mechanics problems lend themselves to using a little intuition. Before starting a problem, read the description of the physical situation and think to yourself "What would I expect to happen here?" Then work through the maths to see if it supports your intuition. If not, stop and think why. Quite often a STEP mechanics question will include an opportunity for you to explain what's going on, so taking the time to think through the motion in a situation puts you in a great position to explain to the examiner the results of your reasoning.

There are only a limited number of techniques you can use. Here's a non-exhaustive checklist of ideas to consider when you start a mechanics question:
  • Does the situation consist of motion with constant acceleration? Use SUVAT equations.
  • Are the surfaces involved smooth? If there's friction, $F=\mu R$.
  • Is the system in equilibrium? Then forces must balance!
  • Is there a collision? Use the principle of Conservation of Momentum. In an inelastic collision, the Coefficient of Restitution tells you how much energy is lost; it's the ratio of the speed after the collision to before.
  • Is there circular motion? In that case, there must be a force acting towards the centre of the circle. Conservation of Angular Momentum will be useful here.
Now you've had the chance to consider some of the important ideas that might come up in a STEP question, your next challenge is to have a look at some past papers, maybe starting with STEP I. Read the question, then have a go at creating the mathematical model necessary to solve it, remembering to draw a big clear diagram and identify which techniques you're going to use!