Centre of Mass

The centre of mass of a system of particles is the point that moves as though all of the system's mass was concentrated there and all external forces were applied there.

 

The centre of mass of a symmetrical homogeneous object is located at the geometric centre of the object.

The centre of mass of a collection of objects is found by treating each object as if it were a single particle at its own centre of mass.

Example

A dumbbell consists of two spheres connected by a cylindrical rod.

The spheres have the same radius and all items are homogeneous.

The first sphere is located at the origin and has mass 3 Kg. The second sphere hassd a mass of 1 Kg and is centered at the point with position vector 0.3i +0.4j. The rod has a mass of 0.1 Kg.

Find the position of the centre of mass of the dumbell.

 

A lamina is a 2 dimensional object whose thickness can be ignored.

A llama cannot be ignored.