In essence, I'll be taking whatever's relevant to Beyblade from probably the first one and a half years or so of a uni physics course. So of course, you won't see a discussion on time dilation since Beyblades tend not to travel at the speed of light. This will be very heavily based on mechanics and kinetics, for obvious reasons.

I'll assume basic mathematics is known (e.g. addition, multiplication, and so on). Where more advanced concepts in geometry, algebra or calculus are involved, I'll take time to explain them.

Quote:Defining a particle

Firstly, I will discuss particles before moving on to more complex things like Beyblades. A particle is something that just occupies a point in space. More complex things are made up of many particles; the laws that describe particles can then be used to describe the complex things.

Mathematical interlude: Vector and scalar quantities

Quantities refer to how much of something exist. A scalar quantity is what we call "one-dimensional"; for example, weight of an attack ring or height of a beyblade. Vectors, on the other hand, have both "how much" and "in which direction". For example, if we say that something is "5 meters to the right", that is a vector quantity: the "how much" is 5, and the "direction" is to the right.

Defining the motion of a particle

We have a physical quantity known as displacement. Displacement is a vector, such as "5 meters to the right". Most vector quantities have an equivalent scalar quantity; the equivalent scalar for displacement is distance. For example, in the above case, we say that the distance away is 5 meters. This may seem trivial, but not in certain cases. For example, say the object does not move in a straight line, but takes a roundabout route to reach the point "5 meters to the right". Hence, the displacement is 5 meters to the right; but the distance is much larger since it took a long path to reach there.

Next, we have the vector "velocity", and corresponding scalar, "speed". This refers to how much the above values change with time. For example, a velocity of "5 meters per second, to the right" means that it moves 5 meters to the right every second. Again, while velocity is directional, speed is not. Thus, if an object moves in a circle, after it makes one round, it's velocity would be zero since it's back to where it started! However, its SPEED is non-zero, obviously.

Finally, we have "acceleration", which is how much the velocity changes with time. When something accelerates, it gets faster. I'll cover this in more detail later.

On the laws of motion

All objects in this world tend to obey Newton's laws when they're travelling at everyday speeds, namely that

1) A physical body will remain at rest, or at constant velocity, unless an external net force is exerted on it.

2) A force acting on an object will cause a change in momentum that is proportional to the strength of the force, and in the direction of the force.

3) Every action has an equal and opposite reaction.

The first two points are self-explanatory. Law 1 means things don't happen unless something makes it happen (i.e. the world makes sense). Law 2 is extremely commonsensical; if you push something, it's not going to come closer to you.

The third law, however, should be clarified. It means that everything comes in pairs.

One important example is the repulsion between the atoms in two surfaces in contact with each other. It results in what is known as the "normal force", not because it normally happens (although this is true). In this case, "normal" uses the mathematical definition "perpendicular to something".

So, say you push a wall. Although you're pushing, your hand does not go through the wall. This is because the wall exerts a force perpendicular to the wall, onto your hand. It would not make sense to be non-perpendicular: When you push straight on at a wall, your hand does not move sideways. At the same time, you may ask, although your hand does not go through the wall, the wall also does not go through your hand! This is because your hand is also exerting a normal force onto the wall, pushing the wall away from it at the same time that the wall is pushing your hand away from it.

Another example would be in gravity. Although many of us are aware that we're being pulled towards the Earth, it's very important to also note that the Earth is being pulled towards us.. This also applies for electric forces. However, these are not very much related to Beyblades as we usually play them, so I will not cover these.

Applications of the laws of motion

Now, we convert the above concepts into mathematical laws so they can be applied to calculations.

Firstly, the first two laws can be summarized to a simple equation,

Force = Mass x Acceleration

The more force you apply to an object, the more it will accelerate (or decelerate). The more massive an object is, the less likely it is to be affected by said force.

So let's say you're launching your Beyblade. You apply a force by pulling on the winder/ripcord. As a result, your Beyblade accelerates until the point where it falls off the launcher: this is the final speed of the Beyblade's spinning at the end of the acceleration.

How do we know this speed? Consider that acceleration is a measure of how much the speed or velocity changes with time. So, firstly, we can find the acceleration if we know the force and it's mass (actually, it's not as simple as this, but since spinning tops are so complex, it'll take a while to work up to it), and then we multiply the acceleration by time to find out how much the speed changed altogether.

Therefore, this brings us to the next commonsensical point! The more force you apply, the faster it'll become! Therefore, the harder you pull your ripcord, the faster your Beyblade will be!

We can apply this to see why long ripcords work better. Let's say you're pulling at the same force throughout, so there's a constant acceleration. But! With a longer ripcord, you'll be pulling it, and hence accelerating it, for a longer period of time! As a result, the final speed will be greater than with a short ripcord. However, it's really important to take note that with good technique, you can attain really fast speeds even with a short ripcord: it's about how you pull it.

I understand all that is rather... daunting to read. But! I'm afraid if I jump straight into serious discussion, many people without appropriate background knowledge will be lost! So, I'll need to know how much to put in, how much to give a miss! The next time I update, I'll be covering on analyzing forces, and what forces are likely to act on a Beyblade, then on momentum and how to do analysis related to momentum. Up to here is mainly background information to lay the groundwork for the discussion on Beyblade.

I'll then proceed to discuss on rotational motion (torque, angular speed, angular inertia, etc.), which, together with the discussion above, will allow for detailed analysis of a Beyblade. I'll also be able to give a lot more examples from here on.

Finally, I'll cover precession, which explains why the Beyblade doesn't just topple over. It's a very horrible topic to explain, but I'll try xD

(I feel like I'm writing a physics textbook.)