Need in depth understanding of Simple physic terms

[jcmartinez]

Hello, i am reading on the Bohr Model. There are some parts i just do not understand.

in classical mechanics, an object, such as an electron, revolving ina circle may assume an infinite number of values for its radius and velocity. Why is this?

Therefore the angular momentum (L= mvr) (? m=mass v=velocity r=radius ?) and the kinetic energy (KE= mv^2/2pi) (? m=mass v=velocity 2pi= something to do with a cirlce ?). again i don't understand why this is.

Bohr then goes to add Planck's quantum theory into his model. This sets conditions on the value of the angular momentum. the angular momentum is quantized according to the following equation: angular momentum = nh/2pi
n= quantum number that could be any positive integer. h is Plancks constant. I am not sure what 2pi is for.

if anyone could please explain these passages to me it would greatly help in my studies. thank you.

 

[Feldoh]

Classically, if we look at a moon orbiting a planet the moon can take on any value radius and velocity because of the way we derive it. Essentially if you work through the derivation there are no restrictions placed on the mathematics. I'm sure you remember doing this at some point if you're learning about more modern physics.

If we start from Newton's laws, or conservation of energy we can derive expressions for momentum, angular momentum, kinetic energy, etc... The derivations are in any introductory physics book.

In the Bohr model, on the other hand, we assume for instance that the angular momentum is quantized. $$L = n \frac{h}{2\pi} = n \hbar$$The two pi is included because we usually write that angular momentum = n times h-bar which is $$\frac{h}{2\pi} = \hbar$$

We use h-bar because if you work with the mathematics a lot there are a lot of 2pi's that pop-up so it's just convenient to lump 2 pi and h into one variable.