Atoms as we know are the structural unit of everything. As i know that atoms are 3D objects, they have length breath and height (they have thickness).Everything is made up of atoms means everything is 3D. So why do we say that any triange ABC drawn on a piece of paper is a 2D figure?

# [Physics] Does second dimension exist? or any other dimension?

atomsdimensional analysis

#### Related Solutions

Most importantly $$ e^{i x} = \cos x + i \sin x$$ only holds (in this form) in radians.

So now you might ask why $e$ is more natural than any other number ;-)

The bigger (and longer) the object, more will be the torque experienced by it. Let's say the length of the chalk we have is $\frac{L}{2}$ (Chalk 1) and $L$ (Chalk 2).

When the chalk falls on the floor, it's most likely to hit on one of its edges. Given that it is dropped from the same height, the force on the heavier mass (Chalk 2) will be more than the one faced by Chalk 1 at one of its edges and on top of that, if we bring torque into the picture, Chalk 2 faces more torque than Chalk 1 on an average because torque is directly proportional to the product of its length from its axis of rotation and force.

Also, the damage from a collision is approximately proportional to momentum aka inertia which is proportional to mass and velocity and proportional to its kinetic energy, which is proportional to its mass and the square of its velocity.

**EDIT**:

About objects falling flat on the ground, the potential energy of the object is used up in breaking the intermolecular bonds in the solid. As larger objects have greater mass, their potential energy tends to be greater so they tend to break the bonds holding the solid together.

If we include air resistance, then it's intuitive that objects with more mass fall harder than a light object. Given that larger objects, in general, are heavier than small objects, we could say the momentum imparted to the larger object is much greater than momentum imparted to the smaller one. So, that could probably explain as to why larger objects break more frequently than smaller objects.

Here's what I think could be the plausible answer (do share your views on it): Smaller objects, in general, have more surface area than volume (magnitude wise). So, the bonds holding the atoms on the surface is well spread which sort of protects the insides pretty well compared to larger objects. When the object falls, due to the larger surface area, the energy transferred to the object is more spread (due to greater surface area to volume ratio). A certain amount of energy is spread out on a larger surface area, therefore the energy density isn't enough to break the intermolecular forces. The object, as a whole, would be relatively safe as to damage the object, we first have to break the surface and given that the surface protects the insides petty well, things are fine for smaller objects. So, I suspect this to be the reason as to why, on average, larger objects tend to break easily.

In the end, it's all about how much mass the object has (which depends on its shape and mass density), the ratio of surface area to volume and how long/big the object is. These all contribute to the severity of the damage faced by the objects.

## Best Answer

You have to make an effort of abstraction. There's no such thing as a first, second, and third dimension. To say that something has a certain number of dimension is (very roughly speaking) to answer the question "How many coordinates do I need to uniquely identify a point on this something?" Like you say, in 3D space we need 3, $x,y,z$. On a sheet of paper you can identify every point with just two numbers (think of drawing a grid of the sheet of paper). Sure the ink on the paper has some finite width, but who cares? When you say "triangle" don't think of a physical piece of something shaped like a triangle. Think of the mathematical object "triangle". Maybe it's simpler if we think circles. If you draw a circle on a sheet of paper, you might again argue that the ink has a width. But what $is$ a circle? A circle is the set of all points $x$ and $y$ such that their distance from another given point (the center) is some fixed number (the radius), i.e. $x^2+y^2=R^2$ where $R$ is the radius.

I will argue that a circle is a one dimensional object. As a matter of fact fixed the radius, you need only one number to position yourself on the circle, specifically an angle $\theta$.

But it makes sense doesn't it? You usually think of a line like a one dimensional object, a circle is just a line curled up a bit. What if we filled the circle and considered the inside too? That would be the set of point $x,y$ so that $x^2+y^2<R^2$. Can you see how many dimensions does this object have?