Spinning top's moment of inertia I (disc on shaft )

[lena_2509]

Homework Statement

Finding the moment of inertia for an Spinning top

Relevant Equations

L = r x F

I hope you guys can help me with this problem..

A top in the form of a flat, circular disc spins on a shaft that is inclined at an angle alpha to the vertical.
Now I have to find the moment of inertia I for the disc about its centre on the shaft.

My attempt was building I with spherical coordinates (r= length of the shaft, phi= \omega t , theta= angle to the vertical) But I think that's just the Point the vector r is pointing to the center of the disc ?

 

[Doc Al]

How about you start with the definition of moment of inertia? (Assuming you need to calculate it from first principles rather than just looking it up.)

 

[lena_2509]

yeah I did it before but my problem is that I don't know how to describe the x y and z values to put them in the moment of inertia
I used the definition below for I and put in the spherical coordinates

 

[Doc Al]

Way too complicated! The moment of inertia of a disk is the same as that for a cylinder. See: Moment of Inertia: Thin Disk

 

[lena_2509]

Way too complicated! The moment of inertia of a disk is the same as that for a cylinder. See: Moment of Inertia: Thin Disk

thank you !
I know that the moment of inertia of a disc is the moment of inertia as a cylinder but how do i discribe the rotation of the disc when it spins on a shaft at an angle alpha?
The shaft of the spinning top would rotate on the coat of a cone i guess...

 

[Doc Al]

but how do i discribe the rotation of the disc when it spins on a shaft at an angle alpha?

I'm not sure how detailed you need to be. Note that in part c they just refer to the direction the top is spinning as $\hat r$.

 

[lena_2509]

I'm not sure how detailed you need to be. Note that in part c they just refer to the direction the top is spinning as $\hat r$.

okay thank you ! maybe I thought too complicated ... thanks a lot !