Centre of Mass
The mass-weighted average position of a system, R = (sum mi ri)/(sum mi), which moves as if all external force acted there.
What is Centre of Mass?
The mass-weighted average position of a system, R = (sum mi ri)/(sum mi), which moves as if all external force acted there.
Key formula / rule: R = (sum mi ri)/M; for continuous bodies use integration.
Key points
- Compute the centre of mass of discrete and simple continuous systems.
- Explain why internal forces cannot move the centre of mass.
Common exam trap
Confusing centre of mass with centre of gravity in a non-uniform field.
Definitions
- Term
Centre of Mass
- Meaning
The mass-weighted average position of a system, R = (sum mi ri)/(sum mi), which moves as if all external force acted there.
- Term
Centre of Mass — explanation
- Meaning
The centre of mass converts a many-particle system into a single effective particle for translational purposes. It need not lie inside the body, as for a ring.
Learning objectives
Compute the centre of mass of discrete and simple continuous systems.
Explain why internal forces cannot move the centre of mass.
Formulae
- Key point
R = (sum mi ri)/M; for continuous bodies use integration.
- Key point
Internal forces cannot shift the centre of mass.
- Key point
It may lie outside the material of the body.
Prerequisites
PHY-U1-NLM-T1-S1-C3
Common mistakes
Confusing centre of mass with centre of gravity in a non-uniform field.
Assuming it must lie within the body.
Keywords
Centre
Practice preview
A bomb at rest explodes into two fragments. What can be said about the motion of its centre of mass immediately after the explosion?…
easy
A uniform square plate of side 'a' has a circular hole of radius R = a/4 cut out from its centre. Where is the centre of mass of the remaining plate?…
medium
A non-uniform rod of length L has a linear mass density lambda = kx, where k is a constant and x is the distance from one end. What is the position of its centre of mass from the end where x=0?…
hard