Why Is Total Mass Used as the Denominator in the Center of Mass Equation?

In summary, the center of mass of an object is calculated by taking the sum of the masses of each component multiplied by their respective coordinates and dividing it by the total mass of the system. This is a weighted average and the denominator is the total mass of the system, not the individual component being calculated. This is because mass is not a vector quantity and does not have components like a force.
  • #1
PsychonautQQ
784
10
so for the center of mass of an object..

x = (m1x1 + m2x2 + ...) / M total
y = (m1y1 + m2y2 + ...) / M total

how come in this equation the denominator is the total mass of the system? It seems like it would make more sense to have the denominator the total mass in whatever component you are trying to figure out...

i feel like it should be
x = (m1x1 + m2x2 + ...) / Mx total

and though i realize this is wrong i was hoping somebody could see what i think i see and explain where my thinking is wrong.
 
Physics news on Phys.org
  • #2
Simply put, it's a weighted average.
 
Last edited:
  • #3
Mass is also not a vector quantity (it has no components like a force, for instance).
 

Related to Why Is Total Mass Used as the Denominator in the Center of Mass Equation?

1. What is the center of mass equation?

The center of mass equation is a mathematical formula used to calculate the point at which an object's mass is evenly distributed in all directions. It takes into account the mass and position of each individual particle in the object.

2. How is the center of mass equation derived?

The center of mass equation is derived from the principle of conservation of momentum and the definition of center of mass as the weighted average position of an object's mass.

3. What is the significance of the center of mass in physics?

The center of mass is an important concept in physics as it helps to describe the motion and stability of objects. It is also used in calculations related to collisions, rotation, and equilibrium.

4. Can the center of mass be outside of an object?

Yes, in some cases the center of mass can be located outside of an object. This occurs when the object has an irregular shape or when there are external forces acting on the object.

5. How is the center of mass equation used in real-life applications?

The center of mass equation is used in a variety of real-life applications, such as designing structures that can withstand strong winds or earthquakes, determining the stability of vehicles, and predicting the trajectory of moving objects.

Similar threads

I A gravity conundrum involving a solid cylinder
    • Classical Physics
Replies
3
Views
985
Center of Mass (Subtraction over addition)
    • Introductory Physics Homework Help
Replies
7
Views
2K
I How does the mass of the wheels affect the car's acceleration?
    • Classical Physics
Replies
15
Views
2K
Center of Mass of separating Orbiting Mass
    • Classical Physics
Replies
2
Views
1K
Finding the center of mass of a simple 2D shape
    • Introductory Physics Homework Help
Replies
9
Views
1K
I Damped oscillator with changing mass
    • Classical Physics
4
Replies
131
Views
4K
Gravitational Forces between two masses
    • Introductory Physics Homework Help
Replies
5
Views
936
Center of mass of spherical shell inside of cone (Apostol Problem).
    • Calculus and Beyond Homework Help
Replies
3
Views
587
The center of mass of a semicircular arc of non-negligible width
    • Introductory Physics Homework Help
Replies
3
Views
847
I Explanation of parallel axis theorem
    • Mechanics
Replies
2
Views
515

Hot Threads

Recent Insights

Back
Top