Moment of Inertia for Composite Object

[theone]

Homework Statement

for this composite object, what moment of inertia needs to be used if you were to sum the moments about the centroid of the object, $$\sum M=I\ddot\theta$$

Homework Equations

The Attempt at a Solution

is it the sum of the $$I_z$$for a solid sphere and a solid cylinder

 

[Simon Bridge]

Was there a question in there?
What makes you think the rotation is about the long axis?
What makes you think the black circle represents a sphere and not a disk?
What makes you think the rectangle represents a cylinder and not a flat block?

 

[theone]

Was there a question in there?
What makes you think the rotation is about the long axis?
What makes you think the black circle represents a sphere and not a disk?
What makes you think the rectangle represents a cylinder and not a flat block?

i am guessing the circle is a hollow sphere and the rectangle a solid cylinder and that the thing rotates about the axis out of the page

 

[BvU]

is it the sum of the $I_z$ for a solid sphere and a solid cylinder

i am guessing the circle is a hollow sphere

Well, some uncertainty there, isn't it ?
Anyway, $$I\equiv\int r^2 dm$$should help you find the right $I$. If that's too much or too complicated, google "parallel axis theorem".

 

[Simon Bridge]

i am guessing the circle is a hollow sphere...

... as opposed to, say, a solid sphere... or a solid disk... what are you basing your guess on?

note: a hollow sphere is commonly represented by a circle while a solid one would be represented by a colored-in circle... but maybe the person setting the question does things differently?

... and the rectangle a solid cylinder...

... why a hollow for the first shape and solid for the second one? Why not the other way around or maybe both hollow or both solid?
It's OK to make educated and informed guesses - but it is never OK to make blind guesses.

...and that the thing rotates about the axis out of the page

... OK. The working you did is for rotating about an axis along the length of the "cylinder". For an axis out of the page, where is the axis of rotation on the figure? The correct moment of inertia depends on it's position. Or, maybe, the question is just asking for which com inertias to apply the parallel axis theorem to? In which case, you want to look more closely at which com moment you have used for the "cylinder".

What I'm getting from your reply is that you do not know which axis is intended or what objects the shapes on the drawing are intended to represent. This is forcing you to make a LOT of assumptions. Bottom line is that you don't have enough information to complete the question as written.

If the question is really so wide open, you will need to make some sort of argument to support your assumptions. Maybe other questions like this one have used hollow spheres and solid cylinders? But maybe what is written above is not the complete problem statement as it was given to you? Right now it is not possible to properly advise you.