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PHYSICS5502
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I am a little bit confused on Center of Mass and Center of Gravity about what are they vectors or scalars . As I may think they are neither because they are simply two points . Am I saying right or wrong .
PHYSICS5502 said:I am a little bit confused on Center of Mass and Center of Gravity about what are they vectors or scalars . As I may think they are neither because they are simply two points . Am I saying right or wrong .
PHYSICS5502 said:I am talking about are they vector quantities.
Points are defined by vectors
PHYSICS5502 said:How are they vector quantities take any frame of your choice and please prove it to me .
https://en.wikipedia.org/wiki/Three-dimensional_space#In_linear_algebraPHYSICS5502 said:A point in 3 dimensional space is a vector ??
PHYSICS5502 said:These things are a little bit difficult to understand but as far as i get, the conclusion for this is that center of mass is position in 3D space so it will have both magnitude and direction .
I would say they are neither. I would say that they are members of an affine spacePHYSICS5502 said:I am a little bit confused on Center of Mass and Center of Gravity about what are they vectors or scalars . As I may think they are neither because they are simply two points . Am I saying right or wrong .
Cutter Ketch said:I think there is some confusion in this thread. In order to specify position we have to compare to something, so we pick an arbitrary coordinate system with an arbitrary origin. Position is then a vector from the origin to the object. However this vector is not an intrinsic physical property of the object. The origin isn't anything real. The position vector is not an intrinsic property of the physical system. This is apparent when you pick a new origin. All the position vectors change even though the physical situation has not. This is distinguished from vector quantities like displacement, force, velocity, or electric field which intrinsically have direction. What's more the associated vector direction and magnitude does not depend on the choice of coordinate system. Those are intrinsically vector quantities. They can't be contemplated without direction. So when someone asks if center of mass is a vector quantity, I think the answer has to be no. It has no intrinsic directional physical property that is invariant under coordinate transform.
PHYSICS5502 said:A point in 3 dimensional space is a vector ??
How can you define the direction of displacement, velocity etc. without an external coordinate system? These quantities don't have an intrinsic direction.Cutter Ketch said:This is distinguished from vector quantities like displacement, force, velocity, or electric field which intrinsically have direction.
But then how can you describe position without direction; only by using a scalar quantity?Cutter Ketch said:Those are intrinsically vector quantities. They can't be contemplated without direction.
Aniruddha@94 said:How can you define the direction of displacement, velocity etc. without an external coordinate system? These quantities don't have an intrinsic direction.
pixel said:I agree with Zapper Z that this discussion has gone too far afield given the level of the question. From the Wikipedia article on center of mass, we have for a collection of n particles of mass mi, total mass M, and position vectors ri:
The center of mass, R, is a vector.
Maybe I wasn't clear enough. Obviously they have direction, but how would you define/specify that direction without an external frame of reference?Cutter Ketch said:They HAVE direction whether you define a coordinate system or not.
But what is down, without a reference frame?Cutter Ketch said:No choice of coordinates will change which direction the force points. Turning your head doesn't prevent the ball from falling down
Aniruddha@94 said:Maybe I wasn't clear enough. Obviously they have direction, but how would you define/specify that direction without an external frame of reference?
But what is down, without a reference frame?
PHYSICS5502 said:I am a little bit confused on Center of Mass and Center of Gravity about what are they vectors or scalars . As I may think they are neither because they are simply two points . Am I saying right or wrong .
Dale said:I would say they are neither. I would say that they are members of an affine space
https://en.m.wikipedia.org/wiki/Affine_space
Affine spaces are definitely closer to vector spaces, but with some subtle differences.
Similarly, Alice and Bob may evaluate any linear combination of a and b, or of any finite set of vectors, and will generally get different answers. However, if the sum of the coefficients in a linear combination is 1, then Alice and Bob will arrive at the same answer.
Thus, we have discovered a major difference between vectors and points:
The notion of linear combination of vectors is basis independent, but the
notion of linear combination of points is frame dependent. In order to salvage
the notion of linear combination of points, some restriction is needed:
The scalar coefficients must add up to 1.
I had not noticed this subtlety before, thanks!robphy said:This is what occurs in the definition of the "center of mass" where the coefficients add up to 1
Aniruddha@94 said:@Cutter Ketch I agree with your statements. In fact I was going to write something similar in my previous post. I get that they have a difference; that the direction for position doesn't even mean anything without a coordinate system, while for the other quantities it does. But is that a good enough reason to say that position is not a vector? I wasn't sure.
Seeing @robphy's post I understand the difference ( it's so subtle).
The center of mass is a vector quantity.
The center of mass is defined as the point at which the mass of an object is evenly distributed in all directions.
Yes, the center of mass can be negative if the object has an uneven distribution of mass.
No, center of mass and center of gravity are not the same. Center of mass is the point where the mass is evenly distributed, while center of gravity is the point where the force of gravity acts on an object.
The center of mass can be calculated by taking the weighted average of the positions of all the particles in an object. It can also be calculated using the formula: xcm = (m1x1 + m2x2 + ... + mnxn) / (m1 + m2 + ... + mn), where xcm is the center of mass and m is the mass of each particle.