Stickboy10
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Hello there I am really struggling with this and another problem and I was hoping you guys could help me out. The problem is as follows:
"the cylinder shown has a radially-dependent density with mass M and radius R. The cylinder starts from rest and rolls without slipping down the incline with height, H. At the bottom of the plane its translational speed is: (8gH/7)1/2
Show MOI of the object is 3/4MR^2."
(this is not a typical shape used in problems. it is going to be something more like a can and I just can't seem how to include the velocity in deriving the equation for I)
My attempt is here:
I = r<sup>2</sup>dm \leftarrow I don't know what dm becomes. I am thinking that \sigma is involved in some way but I don't see where the velocity comes in from there. It may have something to do with density also, but again I can't find a way to connect velocity into that. I may totally wrong and probably am though.
"the cylinder shown has a radially-dependent density with mass M and radius R. The cylinder starts from rest and rolls without slipping down the incline with height, H. At the bottom of the plane its translational speed is: (8gH/7)1/2
Show MOI of the object is 3/4MR^2."
(this is not a typical shape used in problems. it is going to be something more like a can and I just can't seem how to include the velocity in deriving the equation for I)
My attempt is here:
I = r<sup>2</sup>dm \leftarrow I don't know what dm becomes. I am thinking that \sigma is involved in some way but I don't see where the velocity comes in from there. It may have something to do with density also, but again I can't find a way to connect velocity into that. I may totally wrong and probably am though.
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