I can start on the Dynamic parts...perhaps a multi-part post for me...don't have a whole heck of a lot of time right now. At 10, you've likely not had much, if any, exposure to Algebra so this stuff may be a bit hard to grasp. Understandably so. Nevertheless, it's not impossible. I've got my 11 year old daughter learning robotics as we go along. The simple fact that you have a keen interest in this topic and the ambition to reach out and learn will serve you well.
Dynamics
Velocity = circumference * rpm
Velocity is the measure of distance over time. Miles per hour, feet per minute, inches per second, revolutions per minute.
Velocity can be mathematically represented as distance divided by time, or D/t. Think of the "per" above as a divide sign.
Circumference is a measure of distance with respect to a certain constraint, namely a single trip around a circle. In our case, we're talking about wheels, so we call that a revolution.
Looking at the equation above, it is simply converting from revolutions per minute to inches per minute (or centimeters, or whatever you are measuring your circumference with)
So, using some math tricks we can rewrite the above equation, which at 10 you may or may not have learned yet:
Velocity = inches/revolution * revolution/minute
Since the term "revolution" is on both sides of the multiplication sign and one is on the top and the other is on the bottom, they "cancel each other out", leaving "1"s in their place, so you have the following:
Velocity = inches/1 * 1/minute, which simplifies to velocity = inches/minute
Velocity = diameter * pi * rpm OR Velocity = 2 * radius * pi * rpm
Taking the Velocity = circumference * rpm equation, you can substitute the following equations for circumference:
circumference = diameter * pi , or since the radius is 2 times the diameter, you can substitute 2 * radius * pi to get those equations.
To substitute, simply replace circumference in the very first equation with either diameter*pi or 2*radius*pi.
In this example, Admin is showing how to figure out what diameter your wheels need to be in order to achieve a specific set velocity at a specific set revolutions per minute.
So, velocity = 3 feet per second, or 3 ft/s
rpm = 100 revolutions per minute, or 100 r/m
3 ft/s = diameter * pi * 100rpm <-- This equation simply plugs these two values into one of the equations above.
3 ft/s = diameter * pi * 1.67rps (rotations per second) <-- This equation takes the previous equation and converts the revolutions per minute into revolutions per second. This is easily done by dividing by 60. 100 divided by 60 is about 1.67.
diameter = 3 ft/s / (3.14 * 1.67 rps) <-- This equation is a result of moving everything to one side using algebraic fundamentals. Essentially it works off the premise that if you double the size of two equivalent numbers, they remain the same. Or, if you divide two equivilant numbers by the same amount, they also remain the same. Think about it... Then combine it with the "cancel each other out" concept from earlier.
diameter = 0.57 ft, or 6.89" <-- once all the numbers are on one side you can just "do the math". This is simply 3 divided by the result of 3.14 times 1.67. The result will be in feet, so multiply the result by 12 to get inches.
And, with that, I'm done. Gotta get back to work.
Good luck to you. I'm glad to see younger interest in such things. Hopefully I can find my way back to this post and take on the next section. All of this is heavily dependent on you learning Algebra, so that may be something you want to look into in the meantime. In the interest of saving you some time, stick to the basics, because most of this stuff is basic Algebra.
