Calculating the moment of inertia of a filled cylinder

[Thynazgul]

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.

 

[SteamKing]

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?

 

[Thynazgul]

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.

 

[ehild]

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.

 

[HalfLostAndSearching]

I would like to suggest a few steps that can help you in calculating the moment of inertia of a filled cylinder:

1. Understand the concept of moment of inertia: Moment of inertia is a measure of an object's resistance to rotational motion. It depends on the distribution of mass in the object and the axis of rotation.

2. Consider the geometry of the cylinder: In your case, the cylinder is filled with a liquid, so it is not a solid cylinder. You will need to consider the geometry of the cylinder and the distribution of mass inside it.

3. Use the parallel axis theorem: The parallel axis theorem states that the moment of inertia of an object can be calculated by adding the moment of inertia of the object's center of mass and the product of its mass and the square of the distance between the center of mass and the axis of rotation. This can be useful in calculating the moment of inertia of a filled cylinder.

4. Use the formula for the moment of inertia of a solid cylinder: The formula you mentioned, 1/2mr^2, is for a solid cylinder. You can use this formula to calculate the moment of inertia of the empty part of the cylinder and then add the moment of inertia of the liquid using the parallel axis theorem.

5. Consider the viscosity of the liquid: Since the liquid inside the cylinder is viscous, it will resist the motion of the cylinder and affect its moment of inertia. You can use the concept of rotational dynamics to account for the effect of viscosity on the moment of inertia.

In conclusion, calculating the moment of inertia of a filled cylinder is a complex task and requires a thorough understanding of the concept and the geometry of the object. I recommend consulting with your physics teacher or a subject expert for guidance in this matter. Good luck with your extended essay!