What do these images have in common?

Centre of Mass

What is the centre of mass? Most people would find it impossible to walk along such a narrow beam, let alone perform hand-stands and somersaults on it. The secret lies in how you position your weight. Every particle in your body has a small gravitational force acting on it. Together, these forces act like a single force pulling at just one point. This single force is your weight. The point is called your centre of gravity or centre of mass. Keep this point over the beam and you stay on. Move either side of the beam, and your weight produces a turning effect which tips you off.

The weight is acting straight down from the centre of mass. What will happen? The weight is acting straight down from the centre of mass. If the line of action down from the c.o.m. is outside the contact area, the gymnast will fall.

If something wont topple over, its position is stable. Stability If something wont topple over, its position is stable. How stable? The truck is in a stable position. If it starts to tip, its weight will pull it back. As long as the line of action stays above its base, it won’t topple over. This racing car is even more stable than the truck. It has a lower centre of mass and a wider base. It could be tipped over further before it started to topple. Clever stunt driving, but it has put the car in a potentially unstable position. Tip it any further and the line of action will move outside the base. The car will then topple over.

Lines of equilibrium Like the vehicles, the shapes below are all in a state of balance or equilibrium. Why are the shapes stable? Where are their centre of masses? Draw in the lines of symmetry for these regular shapes. Where do you think their centre of mass will be? The centre of mass of a regular shape is where the lines of symmetry cross. Therefore their line of action in the cases above, is inside the base each time. The shapes are in a state of balance or equilibrium.

You cannot draw lines of symmetry onto these shapes. Lines of equilibrium This is fine if you have a regular shape. But how would you find the centre of mass for an irregular shape? You cannot draw lines of symmetry onto these shapes. Think of an experiment you could perform to find out where the centre of mass is located on each shape. Equipment: Paper Scissors Plumb line Discuss with your partner how you might use the equipment to find the centre of mass of each shape.

Lines of equilibrium If card is hung from a thread, the centre of mass is always below, in line with the thread. Repeat the last step from a different point. Centre of mass is where the lines cross. Suspend the card, attach the plumb line. Using a pencil, draw a line along the plumb line.

Finding the centre of mass 1. What is meant by: (a) centre of mass (b) axis of symmetry 2. Draw diagrams of the following shapes and on each indicate the position of their centres of mass. (a) circle (b) square (c) rectangle (d) isosceles triangle 3. Outline an experiment to find the centre of mass of an irregularly shaped piece of card. Carry this out for an irregular shape of your choice. 4. Draw diagrams to explain why it is important that most of the mass of a double-decker bus should be as low down as possible.