Center of mass of an object is the place at which the mass of an object is concentrated. Center of mass is also called as the mass center. In case of a rigid body the center of mass is fixed in relation to the body. The center of mass of an object is used in the calculations of effect of force and torques on an object. This article on how to calculate center of mass will help you in calculating center of mass of different objects.
Calculating center of mass
The formula for calculating center of mass is given as:
This formula is applicable for the discrete masses and in this formula,
- R is the center of mass of a system of particles
- ri is the average of their positions
- mi is the weight of their masses
Another formula for calculating center of mass of the continuous distributed object is given as:
R = (1/M) ∫ r dm
R = (1/M) ∫ mass density × r × dV
- For a continuous distribution, the sum in the above formula becomes integration
- M is the total mass of the body
- In this case the center of mass depends upon the density of the object; if the object has a uniform density then the center of mass of the object is same as the centroid of it (for example: ring, rectangle, spherically symmetrical objects, square, etc)
Example for calculating center of mass of two discrete objects
- To calculate the center of mass of two discrete objects, place two discrete objects.
- Now, choose any arbitrary point from where you want to calculate the center of mass of the objects. This point should be outside of the two objects, but not too far from the objects.
- Now calculate the distance of first object from this arbitrary point and note it down, also calculate the mass of the first object and note it down. Consider this distance as d1 and mass as m1.
- Calculate the distance of another object from this point and note it as d2. Calculate the mass of the object as m2.
- Place these values in the above formula to calculate the center of mass of the two objects.
Suppose the calculated mass of first object is 50 gm and its distance from the arbitrary point is 10 cm, whereas the calculate mass of the second object is 30 gm and its distance from the arbitrary point is 20 cm.
- m1 = 50 gm
- m2 = 30 gm
- d1 = 10 cm
- d2 = 20 cm
Then placing the above values in the formula,
R = 13.75 cm
Therefore, the center of mass of these two objects is located at 13.75 centimeters.
Related Tags: calculating center of mass, calculate center of mass, how to calculate center of mass, center of mass formula, center of mass, calculate the center of mass, center of mass calculator, calculating whole body center of mass
Related Content: