Do linear and angular momentums overlap?

[boris16]

hiya

I hope you can help me.

I've read that angular momentum is not component of linear momentum. But since formula for angular momentum is:

G = r x p = r * p * sin(alpha) = r * p'

p' ... component of linear momentum tangential to radius
p ... linear momentum
G ... angular momentum

From above formulas we can see that one of the quantities that contributes to the final value of angular momentum is also a component of linear momentum p'. Which would suggest that if we were to compute linear momentum for this object from same reference point as we did for angular momentum, then linear momentum's value would also contain a part of angular momentum and vice versa --> value for angular momentum also would contain part of linear momentum.
Wouldn't this suggest that values for linear and angular momentum overlap?

A good analogy of this would be two sets A and B intersecting,

A={1,2,3}
B={1,4,5}


and our job would be to construct a new set which would contain all things that are either members of A or B. Correct thing to do would be to use A u B:

C = A u B = {1, 2, 3, 4, 5}


But instead we create set

C={1, 1, 2, 3, 4} //wrong


that contains two identical elements. I see same situation happening with linear and angular momentums. Their values "overlap".

thank you

 

[neutrino]

What do you mean by "overlap"? Linear momentum and angular momentum can have the same numerical value in some cases, but the vectors representing them are always perpendicular to each other.

 

[boris16]

What do you mean by "overlap"? Linear momentum and angular momentum can have the same numerical value in some cases, but the vectors representing them are always perpendicular to each other.

As far as I'm concerned angular momentum having same direction as rotational axis is just a matter of convenience, since only then does vector not change its direction and as such represents particular property ( constant direction ) of angular momentum. But my math knowledge is not so developed for me to understand why this is not just convenience but instead this vector has all the properties of angular momentum.


All I know is that we derived angular momentum using component of linear momentum.


And unfortunatelly, only way I will understand why linear and angular momentums don't "overlap" a bit is if someone can explain why the fact that we derived angular momentum using component of linear momentum, wouldn't also suggest that the two quantities "overlap".