Centre of Mass
Calculate the centre of mass of a multi body system.
Calculate the centre of mass of a multi body system.
The centre of mass (gravity) is the point at which the whole weight of an object can be considered to act and therefore the point which all parts of an object are in balance.
If the object is supported at the centre of mass there is no NET TORQUE acting
The position of the centre of gravity of an object affects its stability. The lower the centre of gravity (G) is, the more stable the object. The higher it is the more likely the object is to topple over if it is pushed. e.g Racing cars have really low centres of gravity so that they can corner rapidly without turning over.
Increasing the area of the base will also increase the stability of an object, the bigger the area the more stable the object. e.g rugby players will stand with their feet apart if they expect to be tackled.
When an object is tilted it will topple over if its centre of mass falls outside its base.
Below is the formula used to calculate the position of the centre of mass;
Note: you must choose a starting point from which to measure the distances. To simplify this equation choose the C.o.M of one of the objects as your starting point.
If a system experiences no external force, the centre-of-mass of the system will remain at rest, or will move at constant velocity if it is already moving. (Newton's First Law).
We can also consider the Principle of the conservation of momentum where:
The total momentum of a system will remain constant throughout an interaction provided there is no NET external force
The wrench below is thrown in rotation at high speed. The centre of mass can be seen to move in a straight line as the wrench rotates about the C.o.M
This hammer is also thrown in rotation but moving at slower speeds you can see it is acted on by gravity. The path of the centre of mass of the hammer becomes parabolic.
The motorcycle and the rider together form a system. You will notice that the centre of mass (which is to the right of the motorcycle) moves in a parabolic path even though the cyclist and motorcycle are separated.