Velocity of center of mass

By John
2 Min Read

Suppose you take 2 similar tennis balls and put them a bit apart, you see that the centre of mass of the two balls would be their centre. If one of these balls was heavier, the centre of mass will shift towards the heavier ball. But if you take a cricket bat, the centre of mass would be below the centre of the bat, in the lower half. Let us study more about the motion of centre of mass.

Whenever we talk about motion of an object, we usually talk about velocity with which the object is moving or the acceleration with which the object is moving. As we know the centre of mass is denoted by x and y.

X= mi xi /M

Y = mi yi /M

X = Σ mixi
Y = Σ miyi
The position vector of the centre of mass can be written as

Σ miriM
⇒ m1 r1 + m2 r2 +………. +mnrn

Differntiating on both the sides,

M drdt = M1 dr1dt + M2 dr2dt + Mn drndt
Change of displacement of time is the velocity.

mv = m1 v1 + m2v2 +……….. mnvn

where v1 is the velocity of the particle and v = drdt is the velocity of centre of mass.

V = Σ miviM
This is an expression for velocity of centre of mass.