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BodhiAI
Oct. 31, 2019

Centre of Mass:

Centre of Mass :

(i) Position vector of centre of mass for n particle system :

(ii) Position vector of centre of mass for two particle system:

If two masses are equal i.e m1 = m2, then position vector of centre of mass 

(iii) Position vector of centre of mass for continuous mass distribution:

For uniform bodies, centre of mass is calculated using

 

(iv) If a system of particles of massesm1, m2, m3, ……. move with velocities
v1, v2, v3,……, then the velocity of centre of mass

(v) If a system of particles of massesm1, m2, m3, ……. move with accelerations
a1, a2, a3,……, then the acceleration of centre of mass

(vi) Ifis a position vector of centre of mass of a system, then velocity of centre of mass

(vii) Acceleration of centre of mass 

(viii) Force on a rigid body

(ix) For an isolated system, if external force on the body is zero.

i.e., centre of mass of an isolated system moves with uniform velocity along
a straight-line path.