# Centre of Mass

The centre of mass in one dimension is given by $x_{cm}=M_{T}∑_{i=1}m_{i}x_{i} $

The centre of mass in more than one dimension is given by $r_{cm}=∑_{i=1}m_{i}∑_{i=1}m_{i}r_{i} $

For an object with a *continuous mass distribution*, the centre of mass is given by
$r_{cm}=∫_{V}dm∫_{V}rdm $
The above seems complicated, but really it is
$x_{CM}=M1 ∫xdm$
$y_{CM}=M1 ∫ydm$
$z_{CM}=M1 ∫zdm$

# Centroid

- The centroid doesn’t necessarily have to lie on the body
- It will lie on an axis of symmetry
- For homogeneous bodies, the centroid is the same as the center of mass

#gap-in-knowledge https://www.youtube.com/watch?v=SMy8DD2OU8M&ab_channel=PhysicsNinja

### Related

- Used in Linear Momentum