Calculating the moment of inertia of a filled cylinder

AI Thread Summary
The discussion focuses on calculating the moment of inertia for a copper cylinder filled with car engine oil, which is essential for determining its angular momentum as it rolls down a slope. The standard moment of inertia formula, 1/2mr², does not account for the viscous liquid inside the cylinder. The experiment involves measuring various parameters and developing equations to model the cylinder's behavior, comparing theoretical predictions with experimental data. Two models are suggested for the oil's behavior: one where the oil does not rotate and another where it rotates with the cylinder. The goal is to analyze which model better reflects the actual experimental results.
Thynazgul
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Homework Statement


For my IB higher level physics extended essay I will have to calculate the angular momentum of a cylinder rolling down a slope. The cylinder is made out of copper and will be filled with a known mass of car engine oil. I think i can obtain the angular velocity fairly easily since it is just ω=2πF. My problem is with the moment of inertia of this cylinder.

Homework Equations


I know that the equation for moment of inertia is 1/2mr2 but this does not take into account that there is a viscous liquid inside of the cylinder. For angular momentum I will use L=I*ω.

The Attempt at a Solution


I have not tried much because the IB does not include moment of inertia in its syllabus so I am quite lost at the moment.
 
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Thynazgul said:

Homework Statement


For my IB higher level physics extended essay I will have to calculate the angular momentum of a cylinder rolling down a slope. The cylinder is made out of copper and will be filled with a known mass of car engine oil. I think i can obtain the angular velocity fairly easily since it is just ω=2πF. My problem is with the moment of inertia of this cylinder.

Homework Equations


I know that the equation for moment of inertia is 1/2mr2 but this does not take into account that there is a viscous liquid inside of the cylinder. For angular momentum I will use L=I*ω.

The Attempt at a Solution


I have not tried much because the IB does not include moment of inertia in its syllabus so I am quite lost at the moment.

It's not clear what information you have to work with. Can you post the complete text of the problem you are trying to solve?
 
SteamKing said:
It's not clear what information you have to work with. Can you post the complete text of the problem you are trying to solve?
The thing is that this is an experiment I have to perform. I have not been provided with any data but I can measure many things. I can measure mass, radius, velocities, pretty much anything I want. As for the problem, my teacher says that the point of this essay is to come of with a set of equations that can model the behaviour of a cylinder filled with oil rolling down a slope. I then compare my theoretical model with experimental data and see how accurate it was.
 
You can determine the moment of inertia of the empty cylinder. When it is filled with oil, and supposing it is is completely filled, you have two simple models for the behaviour of the oil: The oil does not rotate or the oil rotates together with the cylinder. Neither situation is real, but the experimental results will show which was closer to reality.
 
Last edited:
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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