2. The centre of mass is a point which is the average of all the masses. It can be thought of as a point where the masses would ‘balance’. It can be used as a pretend point to make equations simpler.

3. For simple objects the centre of mass is the middle point. To find a the centre of mass of a more complicated object, or group of objects, you need to use an equation.

4. m 1 x 1 + m 2 x 2 +m 3 x 3 … m 1 + m 2 +m 3 … m is the mass of an object. x is the distance of each mass from a point. x com is the distance of the CoM from the point. You can choose the zero point to be wherever you want. x com =

5. Find the centre of mass of these two balls. They are connected by a thin wire. You can assume the wire has negligible mass. 4kg 7kg 1.8m

6. Firstly we need to choose a zero point to measure our x from. 4kg 7kg 1.8m We could choose here Or here

7. We want to choose the place that makes our equation easier. The best place to pick if you have a choice is the middle of one of the objects. This makes one of our x numbers zero and simplifies our equation.

8. So lets pick the middle of the 4kg ball. 4kg 7kg 1.8m

9. Now we use the equation measuring each x value from the point we picked. Remember, if you measure x in opposite directions one of the x values will be a negative number.

10. m 1 x 1 + m 2 x 2 +m 3 x 3 … m 1 + m 2 +m 3 … = 4 x 0 + 1.8 x 7 4 + 7 = 1.15 The centre of mass is 1.15m in the positive direction from the point we chose. x com =

11. 5kg 7kg 1.4m 1.2kg 6.4kg 2.0m

12. 5kg 7kg 1.4m 1.9m 2kg

13. When you have objects arranged in 2 dimensions work out each dimension separately. 5kg 7kg 1.3m 2.6m 2kg 0. 40m 1.1m