## Rugby, and Newtonian Mechanics

Yesterday we went to Headingley Carnegie to watch a game of rugby union. The match was in the British and Irish cup between Leeds Carnegie and Bristol, Leeds won 24-19, if you’re interested in that sort of thing.

About ten minutes into the second half Leeds brought on a prop forward by the name of Sam Lockwood. Sam is affectionately know as “the human wrecking ball” amongst the Carnegie faithful. The nickname has nothing to do with Myley Cyrus, and everything to do with the way he hits the defensive line, which has a similar effect to a wrecking ball.

Anyway, the first time he got the ball he hit the line in his usual fashion and the impact carried him and three defenders a good ten yards. This prompted a conversation about how he would be the last person we would like to run at us. During the conversation we were discussing that it isn’t purely a size thing, Sam is a big bloke but there are others bigger who don’t hit the line anywhere near as hard. We noted that it was down to the combination of size and speed. He moves much faster than most players his size. It was while discussing a size speed trade off, wondering if a player had an optimal size to speed ratio (I think a negative correlation between someone’s mass and their top speed would be fair assumption), that I realised what I was actually discussing was momentum.

Momentum is the product of mass and velocity (algebraically speaking, p = mv). I taught momentum and impulse before Christmas and didn’t think to use rugby at all, which is strange because I watch a lot of it.

I then thought further about the sport, and it occurred to me that there are tons of opportunities to analyse the mechanics of a rugby match. There is the force a player runs at, their momentum, the impulse, the friction exerted be the studs. The clash mentioned above where Sam Lockwood took three defenders ten yards could form the basis for a whole lesson itself! On top of this there is a huge variety of projectile problems one could look at.

The question of forward passes is an interesting one, and the angle the ball leaves the hand, the velocity of the player, the velocity of the pass, if all these vectors were resolved we could get some interesting results.

I am extremely excited about teaching mechanics now, the next mechanics module I teach is M3, and I intend to find some interesting rugby based problems in the content!

What’s the moment of inertia of an ellipsoidal shell? 🙂

Brilliant question!