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lilphy
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Hello
1. Homework Statement
In a uniform solid cylinder of radius r, mass m and height h we emptied a cylindrical cavity of radius r/4 tangent and parallel to the symmetrical axis z of the original cylinder.
The cylinder is rolling without slipping on a horizontal plane. Find the kinetic energy in terms of θ and θ' where θ is the angle between vertical and the line joining the center of the original solid cylinder and the center of the cavity.
K= 1/2 Icmw²+1/2mvcm²
K=1/2 I w²
I found the moment of inertia I=17/32 m r²
and Icm=17/32 m r² - md²
To find d² I found the z component of cdm = h/2
I don't know which formula is easier to use the first one using Icm and vcm or the second one ?
It is rolling without slipping so w and vcm are related...
But I don't know how yo find w, is it w=θ' * r ?
Thanks
1. Homework Statement
In a uniform solid cylinder of radius r, mass m and height h we emptied a cylindrical cavity of radius r/4 tangent and parallel to the symmetrical axis z of the original cylinder.
The cylinder is rolling without slipping on a horizontal plane. Find the kinetic energy in terms of θ and θ' where θ is the angle between vertical and the line joining the center of the original solid cylinder and the center of the cavity.
Homework Equations
K= 1/2 Icmw²+1/2mvcm²
K=1/2 I w²
The Attempt at a Solution
I found the moment of inertia I=17/32 m r²
and Icm=17/32 m r² - md²
To find d² I found the z component of cdm = h/2
I don't know which formula is easier to use the first one using Icm and vcm or the second one ?
It is rolling without slipping so w and vcm are related...
But I don't know how yo find w, is it w=θ' * r ?
Thanks
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