Sorry i don't know the exact formula but it involves the quantum physics tensorantisymmetric angular momentum operators. it something to do with the ability to generalize advanced mathematics of the universe to arbitrary dimensions i have not tried to do math but i think it just is helicity. angular momentum in 1 dimension simply is a + or a - (and a h-bar/2 constant somewhere i think) that says if its motion is aligned with its spinsor or something. to generalise angular momentum in n-dimensional case is; 1 a + or a - (one level below a scalar) 2 a scalar (just a number with no direction other than + and -) 3 a vector (has direction and value) 4 a tensor (a matrix in this case) that has more than one direction and a value space time geometry or 1 - 3 dimensions a complicated Clifford algebra tensor that i don't want to think of basically in classical mechanics angular momentum is only defined in dimensions of 2 and 3 physicists and mathematicians have generalized it to n-dimensional space but it is not a what you would learn in high school. hope i did OK since i don't even understand all of this but it should at least tell you how complicated it is. try out http:/en.wikipedia.org/wiki/Feynman_checkerboard it is a topic on angular momentum in 1 spacial dimension by some one much smarter than me
angular velocity (omega) = theta/time taken theta is dimensionless i.e. it has no dimensions therefore, the diemnsion of angular velocity is 1/T=T^-1
Momentum = Mass X Velocity Velocity = Displacement/Time Dimension of Mass = M Dimension of Displacement = L Dimension of Time = T Therefore Dimension of Velocity = LT-1 Therefore Dimension of Momentum = MLT-1
The dimension of angular velocity is reciprocal time . . . 1/time or T-1 . It'll be stated as "some angle" per "unit of time", like "45 revolutions per minute", and angles are dimensionless.
case 1 is mass (m) on weightless length (r) of string at constant velocity (v), so angular momentum L = r * (m * v), SI units are n.m.s. or kg.m^2.s^-1 . case 2 is mass(m) rotating around an axis inside its own mass ie solid sphere rotating about its fixed symmetry axis, angular momentum L = I * w, where I is the mass moment of inertia of the sphere about its fixed symettry axis, and w is the rotation in radians per second, units are kg.m^2 for I, and rad / sec for w
[ T-1 ] . Reciprocal time, from "degrees per second" .The angle part of it is dimensionless.
angular velocity (omega) = theta/time taken theta is dimensionless i.e. it has no dimensions therefore, the diemnsion of angular velocity is 1/T=T^-1
Momentum = Mass X Velocity Velocity = Displacement/Time Dimension of Mass = M Dimension of Displacement = L Dimension of Time = T Therefore Dimension of Velocity = LT-1 Therefore Dimension of Momentum = MLT-1
The angular momentum quantum number, symbolized by l, indicates the shape of an orbital.
The "intrinsic angular momentum" of particles is commonly called "spin". The spin of a photon is 1, in the units commonly used.
The dimension of angular velocity is reciprocal time . . . 1/time or T-1 . It'll be stated as "some angle" per "unit of time", like "45 revolutions per minute", and angles are dimensionless.
case 1 is mass (m) on weightless length (r) of string at constant velocity (v), so angular momentum L = r * (m * v), SI units are n.m.s. or kg.m^2.s^-1 . case 2 is mass(m) rotating around an axis inside its own mass ie solid sphere rotating about its fixed symmetry axis, angular momentum L = I * w, where I is the mass moment of inertia of the sphere about its fixed symettry axis, and w is the rotation in radians per second, units are kg.m^2 for I, and rad / sec for w
The angular momentum number shows the shape of the electron cloud or the orbital. The magnetic quantum number, on the other hand, determines the number of orbitals and their orientation within a subshell.
[ T-1 ] . Reciprocal time, from "degrees per second" .The angle part of it is dimensionless.
The principal quantum number n = 3 and the azimuthal or orbital angular momentum quantum number would be l =1 .l = 1
[p]=[wl-1]
n-1 is the max l
"l" is known as the angular momentum quantum number. Principal Quantum Number = n Angular Momentum " " = l Magnetic " " = ml Spin " " = ms (Only possible values are 1/2 and -1/2) Search "Permissible Values of Quantum Numbers for Atomic Orbitals" for the values. You basically have to understand the concepts & be able to recreate the chart for tests, otherwise you can blindly memorize it. The chart should be in your book.