Before we look at the centre of mass formulas lets us quickly look at what the concept means. The centre of mass of a body is defined as a point at which whole of the mass of the body appears to be concentrated. The centre of mass of few useful configurations is given below.
Centre of Mass Formulas
1. A system of two point masses m1r1 = m2r2. The centre of mass lies closer to the heavier mass.
2. Triangle (at the centroid)
3. A semi-circular disc
4. Semicircular ring
5. Hemispherical shell
6. Solid Hemisphere
The height of the centre of mass from the base is h/4 for the solid cone and h/3 for the hollow cone.
Centre of Mass Videos
Problem illustration on Centre of Mass
Motion of the Centre of Mass and Conservation of Momentum
1. Velocity of centre of mass
2. Acceleration of centre of mass
Momentum conservation m1v1+m2v2 =m1v’1 + m2v’2
Elastic Collision= ½ m1v12 + ½ m2v22 = ½ m1v’1 2+½m2v’22
Coefficient of restitution
e=0, completely elestic collision
e=1, completely inelastic collision
If v2=0 and m1≪ m2 then v’1 = -v1
If v2=0 and m1 ≫ m2 then v’2 = 2v1
Elastic Collision with m1=m2 then v’1 = v2 and v’2 = v1