Newton and Mechanics

Isaac Newton is a name that comes up a lot in Physics (an understatement if ever there was one). In Mechanics I tend to lump the SUVAT equations and laws together, teaching them as a small section (effectively) under his name. This blog considers this short section of work.

I usually start with a moment to play the YouTube clip from Big Think, where Neil deGrasse Tyson gives his view on who was the greatest physicist of all time. It is a really nice and brief discussion of how amazing Newton was. It ignores the negative aspects of his life and nature, the arguments with Leibniz ad his ‘followers’ over calculus for example. Sometimes I might comment on this with the students … usually followed by a brief comment about Einstein, Maxwell and Feynman. But on with the work…

The reference is made to the fact that in Mechanics, Newton has his ‘equations of motion’ and his ‘laws’. Students need to know both.

Note: Section 2.1 of the IB Physics Guide refers under the comment about the Nature of Science, that “The kinematic equations for uniform acceleration were developed through careful observation of the natural world”. This is not correct. The equation begins with a definition of acceleration, from which ‘v=u+at’ is written as a simple rearrangement. The rest of the equations are produced by applying calculus and substitution to this – they allow us to describe motion in the natural world, but they were not developed from those observations.

As in my above comment, in considering the equations, I start with acceleration and briefly discuss what this term means. Students usually feel that acceleration means ‘to speed up’, so it is an interesting conversation to discuss the vector nature of velocity, that it has a magnitude (the speed) and a direction, and if either of these changes, the vector has changed. As such, acceleration means…

• To speed up.
• To slow down.
• To change direction.

This trio of points almost becomes a mantra when considering motion.

From the definition of acceleration, it can be integrated to give the equation for ‘s’ (they will likely not know how to integrate yet) and putting these two together, the equation for v² derived. I only do these three. I point out that the data booklet has a fourth which they might like to derive themselves, but point out that the three I have done, are enough to calculate all that is needed.

Then we get to the laws. To give an overview, I state that:

• Newton’s First law is about Motion when the forces are balanced.
• Newton’s Second law is about Motion when the forces are unbalanced.
• Newton’s Third law is about forces being in pairs.

The work now is pretty standard stuff, but it is worth pointing out that the example of Inertia usually involves considering a car travelling around a bend and the fact that the passenger ‘feels’ like they are being forced outwards when in fact, they are being forced inwards. It opens up an interesting debate about our senses and how much we dare trust them – hence part of the need for instruments. You can then have a great conversation about the terms ‘centripetal’ and ‘centrifugal’!

Newton’s second law should be emphasised as the unbalanced force being proportional to the rate of change of momentum, not the more typical, F=ma. This equation can be shown to drop out of the rate of change of momentum, but momentum should be emphasised – it has its own section of the syllabus now and should be viewed as very important. I usually point out that momentum is linked to (1) forces, (2) kinetic energy and (3) it is conserved – hence it is very important.

Newton’s third law I will leave for another time – the trickiest of the laws.