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Centre Of Mass

Consider two particles of unequal mass connected by a massless rod (figure). If a force is applied between the lighter particle and the centre of mass, the system rotates clockwise figure (a). When a force is applied between heavier particle and centre of mass, the system rotates anticlockwise figure (b). When a force is applied at the centre of mass, the system moves in the direction of force without rotation figure (c).

Centre of mass (a) Centre of mass Assignment Help(b) Centre of mass Homework Help(c)

The overall motion of a system can be described in terms of a point called centre of mass. The centre of mass of a system (M) represents translational motion of the system. It moves as if all the mass of the system is concentrated at this point.

The system behaves as if the resultant external force is applied to a single particle of mass M located at the centre of mass.

For a system of two particles

Consider first a system of two particles m1 and m2 having abscissa x1 and x2 respectively from some origin O. We define a point C, the centre of mass of the system, at a position xCM from origin O.

We define xCM as

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… (i)

xCM can be treated as

mass – weighted means of x1 and x2 For particles in 2-D plane,

We define yCM as

Impulse And Momentum Assignment Help … (ii)

Impulse And Momentum Homework Help

We can rewrite equation (i) as

Impulse And Momentum Help

Work Power Energy Help

Now Work Power Energy Assignment Help and Work Power Energy Homework Help are abscissa of particles with respect to C.M. of system.

So, if we choose our origin at C.M. of system

kinematics help

Similarly, kinematics help online

For a system of many particle in three dimensions the position of centre of mass w.r.t. any fixed axis is determined form

kinematics Assignment Help

Similarly for y- and z-coordinates of the centre of mass, we may use the equations

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In vector notation, the position vector of centre of mass is

impulse and momentum

kinematics formulas

kinematics formulas Help

kinematics formulas Assignment Help

where kinematics formulas Homework Help is the position vector of the ith particle

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