Yes that’s right! This is my 50th getintophysics blog post! And so to celebrate in true style we will (drumroll please) find the centre of mass of L – fifty in Roman numerals for those at the back.
Centres of mass are important because they help us model things more simply. For example, if we wanted to track a ball through the air, we could easily find the centre of that ball and say that that’s a good approximation of what the ball does. But with shapes that are a bit more complicated, sometimes we want to make things as simple as possible and reduce the object to a single point at the centre.
But where is the centre of an oddly-shaped item like an L? How do you work out the middle? And what if it’s heavier in one spot than another? That's where the centre of mass comes in.
Let’s start with a simple shape, an equilateral triangle. Using a drawing pin, a string attached to it and a board on the wall, loosely pin the triangle to the board by one of its points. It will hang freely and come to rest. Then use the vertical string as a guide for a ruler to mark a straight line vertically downwards from the pin.
Then repeat with two more points – easy when you have a triangle! So you get a spot where they have all intersected. Congratulations, you have the centre of mass!
Doing irregular shapes works in just the same way, choose three points (quite far apart is best) and use the vertical line to create three intersecting lines. It’s often quite surprising where the centre of mass is! You can try this easily at home by taking a piece of paper, cutting a random shape and then use the method.
It has to be said, for a 50th post celebration, L is quite a tricky letter. I blame the Romans. That’s because once you get started you’ll see that the intersection isn’t actually on the shape itself. But don’t let that stop you. Use tracing paper or something else you can see through, trace the outline of the L on to it. Then when you hang the shape, you can line the tracing paper up and mark the vertical lines on the tracing paper instead.
Hurrah! 50 posts and the centre of mass of 50 (in Roman numerals)!