Before we look at the centre of mass formulas lets us quickly look at what the concept means. Centre of mass of a body is defined as a point at which whole of the mass of the body appears to be concentrated. Centre of mass of few useful configurations are 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.
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