HELP : Centre of mass and Centre of gravity

In summary, the centre of mass and the centre of gravity are often used interchangeably, but they are not exactly the same thing. The centre of mass is the point where the net gravitational force can be considered to act on an object, while the centre of gravity is the point where the net gravitational torque can be considered to act. These points may coincide for a constant force of gravity, but they are not necessarily always the same. The position of the centre of gravity can be calculated using a formula involving the net force and torque acting on an object.
  • #1
garyljc
103
0
hello ,
could anyone explain to me the difference between
a.) the centre of mass
b.) the centre of gravity

much aprreciated =) Cheers
 
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  • #2
There isn't really any.

The terms are just used differently depending on context, but it's the same thing
 
  • #3
No, they are not the same.
The centre of gravity is the point (if it exists) so that if the net gravitational force acting upon the object is considered to act at that point (rather than diffusely distributed at the various mass points the object consists of), then the torque wrt. the C.M of the object is the same as the torque (wrt. C.M.) as calculated for the diffusely distributed gravitational force.

Evidently, for a constant force of gravity, the C.M and the C.G coincide.
 
  • #4
hmmm sorry but I'm stll a lil confuse , could elaborate slightly more =)
 
  • #5
garyljc said:
hmmm sorry but I'm stll a lil confuse , could elaborate slightly more =)

see, this is why my explanation was better.

Don't worry about the differences, they're essentially the same thing
 
  • #6
They are not the same thing.
As measured from the C.M of the object, where [itex]\vec{F}[/itex] is the net (grav.)force on the object, and [itex]\vec{\tau}[/itex] is the net (grav.) torque wrt. to the C.M, we have that that the position of C.G, [itex]\vec{r}_{C.G}[/itex] is given by the formula:
[tex]\vec{r}_{C.G}=\frac{\vec{F}\times\vec{\tau}}{|\vec{F}|^{2}}[/tex]
under the condition [itex]\vec{F}\cdot\vec{\tau}=0[/itex]

It by no means follows that we have [itex]\vec{r}_{C.G}=\vec{0}[/itex]
 
Last edited:

What is the difference between centre of mass and centre of gravity?

The centre of mass is the point at which the entire mass of an object can be considered to be concentrated, while the centre of gravity is the point at which the entire weight of an object can be considered to be concentrated. In most cases, these two points are the same, but they can differ if an object is subject to external forces such as gravity or friction.

How is the centre of mass calculated?

The centre of mass can be calculated by finding the average position of all the individual particles that make up an object. This can be done by multiplying the mass of each particle by its distance from a reference point, and then dividing the sum of these values by the total mass of the object.

What factors affect the centre of mass?

The centre of mass of an object is affected by its shape, size, and distribution of mass. Objects with irregular shapes or varying densities will have a more complex centre of mass, while objects with symmetrical shapes and uniform density will have a centre of mass that is easier to determine.

Why is the concept of centre of mass important?

The centre of mass is an important concept in physics as it helps us understand how objects behave under the influence of external forces. It is also used in engineering to design stable structures and in sports to improve performance and balance.

Can the centre of mass be outside of an object?

Yes, the centre of mass can be outside of an object, especially if the object is irregular or has a hollow interior. In these cases, the centre of mass may be located at a point where there is no actual mass, but it is still a useful concept for understanding the overall behaviour of the object.

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