# Experimental value for moment of inertia - Not about c.o.m.

## Homework Statement

These are the pre lab tasks for my upcoming lab. Find the theoretical value for moment of inertia for a ring with off axis rotation using parallel axis theorem and outline procedure to obtain experimental value of I.

During the lab we will be using a rotating platter with a disc of known weight and radius on the bottom. It will be spun and we will drop a ring of known weight and radii on top with the inner radius touching the axle about which everything is being rotated. So the lower disc will be spinning about centre and ring will be spinning off axis. There will be a computer measurement of angular velocity before and after ring has been dropped onto disk.

## Homework Equations

Iparallel = Icm + m d2
L = I ω

## The Attempt at a Solution

The formula I found for theoretical value for moment of inertia is I = Idisc + ( Iring + m (inner radius)2)
Where I'm at a loss is how to experimentally find a value for the moment of inertia of the ring. My first attempt was to use angular momentum (L = I ω) thinking it would be conserved but looking a the equations, having different theoretical values for I tells me thats not the case. We have not touched on this in class and I'm unsure of what direction to go.

Any help at all with some guidance and equations to use is greatly appreciated I've just feel like I've hit a brick wall.

SammyS
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## Homework Statement

These are the pre lab tasks for my upcoming lab. Find the theoretical value for moment of inertia for a ring with off axis rotation using parallel axis theorem and outline procedure to obtain experimental value of I.

During the lab we will be using a rotating platter with a disc of known weight and radius on the bottom. It will be spun and we will drop a ring of known weight and radii on top with the inner radius touching the axle about which everything is being rotated. So the lower disc will be spinning about centre and ring will be spinning off axis. There will be a computer measurement of angular velocity before and after ring has been dropped onto disk.

## Homework Equations

Iparallel = Icm + m d2
L = I ω

## The Attempt at a Solution

The formula I found for theoretical value for moment of inertia is I = Idisc + ( Iring + m (inner radius)2)
Where I'm at a loss is how to experimentally find a value for the moment of inertia of the ring. My first attempt was to use angular momentum (L = I ω) thinking it would be conserved but looking a the equations, having different theoretical values for I tells me that's not the case. We have not touched on this in class and I'm unsure of what direction to go.

Any help at all with some guidance and equations to use is greatly appreciated I've just feel like I've hit a brick wall.
Yes, you are to do this assuming conservation of angular momentum.

You have different moments before and after, and you have different angular velocities, Right ?

• scottymo
haruspex
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You have different moments before and after, and you have different angular velocities, Right ?
To clarify, different moments of inertia before and after.

• scottymo
To clarify, different moments of inertia before and after.
So my angular momentum will be conserved even though I'm going from a disc rotating about its centre of mass to a system of the ring and disc not rotating about it's centre of mass?

Following that I'd just calculate L of spinning disc with initial ω, then subtract L of disc after collision, whats left being put into L = I ω to solve for I of off axis ring?

If it's that simple I'm going to beat my head into the desk for the time I've spent overcomplicating...

haruspex
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So my angular momentum will be conserved even though I'm going from a disc rotating about its centre of mass to a system of the ring and disc not rotating about it's centre of mass?
Yes, but be careful. In most cases, angular momentum is only meaningful in respect of a given axis. This will be conserved as long as the only external forces on the system act through that axis. What is a possible source of external forces on the disc+ring system, in the plane of rotation, when, and after, the ring is dropped?
Following that I'd just calculate L of spinning disc with initial ω, then subtract L of disc after collision, whats left being put into L = I ω to solve for I of off axis ring?
Yes.

• scottymo
Yes, but be careful. In most cases, angular momentum is only meaningful in respect of a given axis. This will be conserved as long as the only external forces on the system act through that axis. What is a possible source of external forces on the disc+ring system, in the plane of rotation, when, and after, the ring is dropped?

Yes.
Perfect thank you for the help. And yes theres the friction of collision before the surfaces reach the same speed, bearing friction, moment upon the axle, and air resistance.

haruspex
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Perfect thank you for the help. And yes theres the friction of collision before the surfaces reach the same speed, bearing friction, moment upon the axle, and air resistance.
I was thinking of something quite specific, that doesn't go away even when friction etc. are ignored. You mentioned moment upon the axle... not sure what you mean but it could be what I have in mind.