Treating the object as material point in kinematics

[Femme_physics]

Treating the object as "material point" in kinematics

From the kinematics questions I need to solve, I notice a lot of time they mention to treat the moving object as a "material point" (I translate how they write it in Hebrew). I wonder exactly what is the meaning of it? Do the kinematics formulas not apply on non-material points? And what are non-material points, exactly?

 

[I like Serena]

From the kinematics questions I need to solve, I notice a lot of time they mention to treat the moving object as a "material point" (I translate how they write it in Hebrew). I wonder exactly what is the meaning of it? Do the kinematics formulas not apply on non-material points? And what are non-material points, exactly?

That would be "point mass".

Your objects are treated as mathematical points.

In reality of course these do not exist.
For instance a basket ball has a definite size.

Size introduces 2 new problems:

The ball itself will rotate, which will take part of the energy.
(That's where moment of inertia comes in.)

When checking if the ball will stay out of reach of a goal tender, you need to consider the size of the ball and it won't suffice to see that it's trajectory is out of reach.

 

[Femme_physics]

That would be "point mass".

Your objects are treated as mathematical points.

In reality of course these do not exist.
For instance a basket ball has a definite size.

Well, a basketball is kinda like a point, if a point is a circle...a basketball is circle! (well, it's just got some volume, but a circle nonetheless!)

By the transitive property I must be right :)But seriously,
I mean, what would be an example of a "point mass" RL object? Or is it just an ideal object with...well...how much mass does this "point mass" have? One?

(That's where moment of inertia comes in.)

Never heard that term. Mommint uf een-hertz-ya?

;)

 

[I like Serena]

Well, a basketball is kinda like a point, if a point is a circle...a basketball is circle! (well, it's just got some volume, but a circle nonetheless!)

By the transitive property I must be right :)But seriously,
I mean, what would be an example of a "point mass" RL object? Or is it just an ideal object with...well...how much mass does this "point mass" have? One?

A basketball is also kind of like a... rabbit! :)

EDIT: And a square is like a glass bead necklace that you hold up in a sort of square formation.
(I gave one to micromass, and he liked it a lot after some discussion. ;)Uhh, a small piece of lead that you throw somewhere?

The mass of a point mass can be anything.
IRL many objects are (at least at first) treated as a point mass.
So a car can be treated as a point mass. It would have a mass of about 1000 kg.

All the regular dynamics/kinematics formulas will work just fine, until you go into more detail, and start looking how the tires are turning and how the chassis might deform.

Never heard that term. Mommint uf een-hertz-ya?

;)

And I thought you would have trouble understanding the concept of a goal tender!

;)

EDIT: And you wouldn't remember, it's only where we met many ages ago!

 

[Femme_physics]

All the regular dynamics/kinematics formulas will work just fine, until you go into more detail, and start looking how the tires are turning and how the chassis might deform.

But a point mass must have a shape, no? Is it a circle? Or, is it just "mass whose moment of inertia/shape/volume/ etc not taken into consideration"?

EDIT: And you wouldn't remember, it's only where we met many ages ago!

Ah yes...the "legendary question".. ;)

 

[I like Serena]

But a point mass must have a shape, no? Is it a circle? Or, is it just "mass whose moment of inertia/shape/volume/ etc not taken into consideration"?

It's a mathematical abstraction that does not exist.

Suppose you draw a circle on a piece of paper.
There- you have a circle.

Now do it again, put the point of your pen on the paper.
Wait! Stop! Do nothing else!
There- you have a point! In practice, objects are modeled as point masses, meaning: "mass whose moment of inertia/shape/volume/ etc not taken into consideration". :)

 

[Femme_physics]

It's a mathematical abstraction that does not exist.

Oooh...beautiful wording.. "mathematical abstraction"...that's how you get the girls eh? :)

In practice, objects are modeled as point masses, meaning: "mass whose moment of inertia/shape/volume/ etc not taken into consideration". :)

Wow, that's an even better wording. Who came up with that?!? That person is a genius. I must meet that person. Best forum quote ever. Definitely without a shred of single doubt (okay I'll stop... :) )

 

[I like Serena]

Oooh...beautiful wording.. "mathematical abstraction"...that's how you get the girls eh? :)

Only you! :!)

 

[Femme_physics]

:)

I love the lead-up to your explanation, with the pencil.. lol... both funny and brilliant ;)
Keep it up!

 

[I like Serena]

:)

I love the lead-up to your explanation, with the pencil.. lol... both funny and brilliant ;)
Keep it up!

:)

I will if you do ;)

 

[AlephZero]

If you haven't met the term "moment of inertia" yet, then you haven't studied the mechanics of objects that are rotating.

The motion of a finite sized rigid body can be described by two things which are pretty much independent of each other. One is the linear motion (translation) of its center of mass, the other is its rotation about its center or mass.

Rotational motion obeys Newton's laws of motion, so there isn't really anything "new" involved, but rather than going back to first principles all the time it is easier to work with concepts like angular velocity and acceleration, torque, and moment of inertia. The equivalent of
force = mass times acceleration
is
torque = moment of inertia times angular acceleration.

For "small" objects the rotation effects usually become less important than the translation. For eaxmple if you have spheres made of the same material (i.e. the same density) but different radii, the masses are proportional to r³ but the moments of inertia are proportional to r⁵

A "point mass" is just the (theoretical) limiting case where you can ignore the rotation completely.

 

[Femme_physics]

Thanks AZ. I actually did study about it, I was just making an "inside joke" with ILS since he helped with with a few of those! :)

 

[Studiot]

I can see where those whose first language is not English could have difficulty with some expressions so here are some extracts that might help.

A ‘material point’ is a ‘particle’. Particle is probably a more generally used term.
You will find it in many areas of science and technology.


https://www.physicsforums.com/showthread.php?t=386051&highlight=particle
posts 38 – 44

My answer to what is a particle goes right back to Dalton (and perhaps even the ancient Greeks).

A 'particle' can be as large as a cup of coffee or a planet.
Or it can have zero dimensions.
It all depends what we are talking about.

From the point of view of chemical bonding, molecules (if you allow single atom molecules) are the 'particles' - smallest elements - that can participate.

From the point of view of fluid dynamics ( and indeed any continuum theory) we take a
'control volume' and in the limit shrink it to a point. These are the Fluid 'particles'.

From the point of view of Finite Element Analysis the 'particles' are the mesh spaces. These always have real defineable size.

From the point of view of the coffee trolley the 'particles' are the cups of coffee brought into the office...

What I am really saying is that the concept is about divisibility - What is the smallest element within which a subject or model of interest can operate such that if I divide it further my model is no longer valid. My subject can be material (mass, volume etc) or it can be non material (gravity) or even just a concept.

https://www.physicsforums.com/showthread.php?t=401819&highlight=particle
Post #53
(after Glauert)

A particle is often said to be a point mass with no spatial extent. Atomic nuclei and electrons might be thought of as particles of this type, but Newton’s laws are not intended to apply to such small scale phenomena; usually quantum mechanics must be used instead. In classical mechanics the smallest piece of matter we need to consider contains enormous numbers of atoms and on this scale we can ignore atomic structure and think of matter as continuous.
Accordingly, we define a particle to be a material body whose dimensions, though not zero, are sufficiently small for the internal structure of the particle to be unimportant. The actual size permissible depends upon the particular physical problem. Thus the Earth may be treated as a single particle for the discussion of its movement around the sun, but a grain of sand cannot be treated as one in the formation of a sand dune. For our purposes the essential feature of a particle is that its position is sufficiently described by a single vector r, the position vector from some origin