Finding Kinetic Energy of a Rotating Object

[ttbmtk6]

Homework Statement

For my High School AP Physics class, we need to build an engine to convert heat to mechanical energy. As such, my team has built a Stirling engine. However, we need to calculate the energy and efficiency of the engine. We're using a peanut butter jar lid as the flywheel, and so we need to calculate the kinetic energy of that.

Homework Equations

KE=1/2mv^2
KE=1/2Iw^2

The Attempt at a Solution

We're pretty sure the best way to find the KE is by using KE=1/2mv^2 and converting it to a rotational form to get KE=1/2(I)(w^2), where I is moment of inertia and w is angular velocity. I imagine that to find angular velocity we should just count how often the lid goes around, but I'm pretty lost on the moment of inertia.

 

[rock.freak667]

If you can measure the thickness of the lid, you can just use I for a disk or a cylinder depending on how accurate you want to be.

For you can do it more accurately and find I for the entire object as it if it were solid and then subtract I for the hollow parts.

 

[ttbmtk6]

How do you find I? And would it be easier then to use something for the flywheel that is only a disk and not a cylinder as well, like a cd?

 

[SammyS]

For a disk of radius, R, and mass M_d, the moment of inertia is : I_d = (1/2)M_d(R²).

For a ring of radius, R, and mass M_r, the moment of inertia is : I_r = M_r(R²).

For the combination: I_Lid = (M_d·I_d + M_r·I_r)/(M_d + M_r)

Other than cutting up an identical (you hope) lid, you could try to find I experimentally.

 

[gneill]

Or, do something clever like making a physical pendulum of the lid and determine its period of oscillation and hence its moment of inertia about the support point. Then use the parallel axis theorem to find the moment of inertia about the center (which corresponds to the center of mass).

http://hyperphysics.phy-astr.gsu.edu/hbase/pendp.html"

http://en.wikipedia.org/wiki/Parallel_axis_theorem"

 

[ttbmtk6]

Why are the equations for the moment of inertia of a disc and a ring the same?

 

[SammyS]

Why are the equations for the moment of inertia of a disc and a ring the same?

Cut & Paste - TYPO !
I'll change it. - DUH at me.