Distribution of mass and angular momentum

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The distribution of mass in two cylinders affects their angular momentum when rolling down an incline. Cylinder one, with mass distributed around an outer radius, will have a greater moment of inertia compared to cylinder two, which has mass concentrated near the inner radius. Consequently, cylinder two will have a higher angular momentum for the same rotation rate due to its lower moment of inertia. To solve for angular momentum (L), the actual mass distribution must be known, as it directly influences the moment of inertia calculation. Understanding these principles is crucial for accurately determining the angular momentum of each cylinder.
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If I had two cylinders of equal weight and size, but cylinder one had the weight distributed around an outer radius and cylinder two had it distributed around an inner one, would it change their angular momentum going down an incline? Would they be equal, or would cylinder two have greater momentum? And how would I reflect this when solving for L?
 
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The moment of inertia of a body is calculated by integrating dm r2, where dm is an element of mass and r is its distance from the axis of rotation. Thus, when mass is close to the axis (your cylinder two), the MI is less, so for a given rotation rate the angular momentum is less.
To calculate it you will need to know the actual mass distribution.
 
Thanks!

For the problem itself, I will have numbers for the mass, which is distributed equally around the center of the cylinder, so will be able to calculate the actual momentum.
 

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