Center of Mass

Centre of mass

It is a point of a body or system at which the whole mass of body or system is supposed to be Concentrated for dealing its translation motion.

Properties of center of mass

(1) Three may or may not be any mass present physically at center of mass. So its position depends on shape of the body.

(2) For a given shape it depends on the distribution of mass within the body and is closer to massive part.

(3) If we apply the external force on cm then we will get maximum results

TO LOCATE CENTRE OF MASS

x- Coordinate of CM

 

y-Co-ordinate of CM

 

z-Co- ordinate of CM

 

Similarly in terms of position Vector

 

Example

Step1. Choose your origin (try to fix your origin at extreme left and lower end)

Step 2. Use above results e.g. x_cm, y_cm etc.

 

 

 

 

POSITION OF CENTRE OF MASS Arc of thin ring

 

0  

 

 

 

PART OF THE DISC

 

 

 

 

LOCATION OF C.M OF SOME HOMOGENEOUS RIGID BODIES

(1) Semi Circular ring

(2) Semi Circular disc

(3) Hollow hemisphere

(4) Solid hemisphere

(5) Cone (Hollow)

(6) Solid cone