Centre of Mass
“Centre of mass of a system is such a point where an applied force causes the system to move without rotation”
It is observed that the centre of mass of a system moves as if its entire mass is confined at that point. A force applied at such a point in the body does not produce any torque in it i.e. the body moves in the direction of net force F without rotation.
Consider a system of two particles A and B connected by a light rigid rod.Let O is a point anywhere between A and B such that the force F is applied at point O. If the system moves in the direction of force F without rotation, then point O is the centre of mass of the system.
does the system still move without rotation if the force acts elsewhere on it?
- let the force be applied near the lighter particle. The system moves as well as rotates.
- let the force be applied near the heavier particle.In this case, also the system moves as well as rotates.
Centre of Gravity
“A point where the whole weight of the body appears to acts vertically downward is called centre of gravity of a body.”
A body is made up of a large number of particles as illustrated. Earth attracts each of these particles vertically downward towards its centre. The pull of the Earth acting on a particle is equal to its weight. These forces acting on a particles of a body are almost parallel forces is a single force equal to the weight of the body. A point where this resultant force acts vertically towards the centre of the Earth is called the centre of gravity G of the body.
It is useful to know the location of the centre of gravity of a body in problems dealing with equilibrium.
Centre of Gravity of an Irregular shaped thin lamina:
A simple method to find the centre of gravity of a body is by the use of a plumbline. A plumbline consists of a small metal bob (lead or brass) supported by a string. When the bob is suspended freely by the string, it rests along the vertical direction due to its weight acting vertically downward. In this state, centre of gravity of the bob is exactly below its point of suspension.
Take a irregular piece of cardboard. Make holes A,Band C,near its edge. Fix a nail on a wall. support the cardboard on the nail through one of the holes (let it be A), so that the cardboard can swing freely about A. The cardboard will come to rest with its centre of gravity just vertically below the nail. vertical line from A can be located using a plumb line hung from the nail. Mark the line on the cardboard behind the plumb line. Repeat it by supporting the cardboard from hole B. The line from B will intersect at a point G. Similarly, draw another line from the hole C. Note that this line also passes through G. It will be found that all the vertical lines from holes A,B and C have a common point G.This common point G is the centre of gravity of the cardboard.