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Centre of Mass

Centre of Mass. CoM. 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. Finding the CoM.

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Centre of Mass

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  1. Centre of Mass

  2. CoM 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. Finding the CoM 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. m1x1 + m2x2 +m3x3… m1+ m2+m3… m is the mass of an object. x is the distance of each mass from a point. xcom is the distance of the CoM from the point. You can choose the zero point to be wherever you want. xcom =

  5. Example 1 Find the centre of mass of these two balls. They are connected by a thin wire. You can assume the wire has negligible mass. 1.8m 4kg 7kg

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

  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. m1x1 + m2x2 +m3x3… m1+ m2+m3… = 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. xcom =

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

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

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

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