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lmnt
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The problem statement
Icm=[tex]\frac{2}{5}[/tex]mr2
[tex]\omega[/tex]=v/r
m=mass of object
There's some things I don't really get about total angular momentum in a rigid body. Suppose a perfectly spherical object is rolling in uniform circular motion (ie. in a loop). Find the total angular momentum.
L=mvr for particle, and L=Icm[tex]\omega[/tex] for rigid body
3. Attempt at solution
Since it is rolling, it has angular momentum due to its own rotation around its axis, like a normal object that's just spinning right? So then L = Icm[tex]\omega[/tex] and I would use [tex]\omega[/tex]=v/r with r=radius of sphere
But then, it also has angular momentum around the centre of the loop-the-loop that it rolls around. Here's where i get lost. Would i consider the object as a particle and use L=mvr, or do i use L = Icm[tex]\omega[/tex] again, and which radius do i use when i sub in for [tex]\omega[/tex]? the radius of the loop or the radius of the mass itself?
I get that the total angular momentum for a situation like this would require adding together the separate momentums but i don't get how exactly they are seperated.
Icm=[tex]\frac{2}{5}[/tex]mr2
[tex]\omega[/tex]=v/r
m=mass of object
There's some things I don't really get about total angular momentum in a rigid body. Suppose a perfectly spherical object is rolling in uniform circular motion (ie. in a loop). Find the total angular momentum.
Homework Equations
L=mvr for particle, and L=Icm[tex]\omega[/tex] for rigid body
3. Attempt at solution
Since it is rolling, it has angular momentum due to its own rotation around its axis, like a normal object that's just spinning right? So then L = Icm[tex]\omega[/tex] and I would use [tex]\omega[/tex]=v/r with r=radius of sphere
But then, it also has angular momentum around the centre of the loop-the-loop that it rolls around. Here's where i get lost. Would i consider the object as a particle and use L=mvr, or do i use L = Icm[tex]\omega[/tex] again, and which radius do i use when i sub in for [tex]\omega[/tex]? the radius of the loop or the radius of the mass itself?
I get that the total angular momentum for a situation like this would require adding together the separate momentums but i don't get how exactly they are seperated.
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