Inertia - Moments of Inertia of a rigid body (different axes)

[frownifdown]

Inertia -- Moments of Inertia of a rigid body (different axes)

Here is the problem http://imgur.com/pL6Bdgw


So I missed class today because I was studying for a genetics test. I don't need the answer or anything but I was wondering what the general rule for inertia that I would use for solving this problem. I looked up some inertia rules but don't really see how they apply. Thanks in advance

 

[berkeman]

Here is the problem http://imgur.com/pL6Bdgw


So I missed class today because I was studying for a genetics test. I don't need the answer or anything but I was wondering what the general rule for inertia that I would use for solving this problem. I looked up some inertia rules but don't really see how they apply. Thanks in advance

The general concept is the "moment of inertia". Look up that formula, and the problem should be straightforward.

 

[frownifdown]

The general concept is the "moment of inertia". Look up that formula, and the problem should be straightforward.

Alright so I looked it up and saw the equation for it (I=mr^2 correct?). Now the problem says to ignore the mass so do I just count the distance from each ball to each axis and square and add them? That seems very tedious. Can you get it from just looking at them?

 

[Doc Al]

Alright so I looked it up and saw the equation for it (I=mr^2 correct?).

Right. That's the moment of inertia for a point mass, which is what you need.

Now the problem says to ignore the mass so do I just count the distance from each ball to each axis and square and add them?

Yes. (You are ignoring the mass of the rods, not the balls.)

That seems very tedious. Can you get it from just looking at them?

Get busy! (No shortcuts.)

 

[berkeman]

Alright so I looked it up and saw the equation for it (I=mr^2 correct?). Now the problem says to ignore the mass so do I just count the distance from each ball to each axis and square and add them? That seems very tedious. Can you get it from just looking at them?

It says to ignore the masses of the interconnecting rods. So yes, you do the sum of the mr^2 number about each axis to get the total I for each axis. Ignore the masses that are on-axis for this problem. It should go pretty fast... EDIT -- Doc is quicker on the draw than I am, again!

 

[frownifdown]

Alright, so I went through and thought I did it right but apparently not. I got G>D>A>F>E>B=C

Edit: I just went back and realized that my value for C was wrong, and it should be 16 instead of 7. I'm unsure on how to add and if there should be negatives though. For instance, would B be 7 or 1? Would I add the 4 on top and subtract 3 from the bottom or would they all contribute 1 to it.

Nevermind, Solved! Thanks everyone

 

[berkeman]

Alright, so I went through and thought I did it right but apparently not. I got G>D>A>F>E>B=C

Edit: I just went back and realized that my value for C was wrong, and it should be 16 instead of 7. I'm unsure on how to add and if there should be negatives though. For instance, would B be 7 or 1? Would I add the 4 on top and subtract 3 from the bottom or would they all contribute 1 to it.

There are no subtractions in MOI calculations...