Mass moment inertia of object displaced from axiz

AI Thread Summary
The discussion focuses on calculating the mass moment of inertia for an object displaced from its axis of rotation. The user considers two methods: developing an integral for mass distribution or using the parallel axis theorem. The consensus leans towards using the integral approach, as it simplifies the computation given the object's orientation. The parallel axis theorem is acknowledged but deemed more complex for this scenario. Overall, the integral method is recommended for its straightforwardness in this context.
PTC
Messages
2
Reaction score
0
Hey y'all,

A plea for general advice here as I embark on a project. Say I have an object rotating around an axis but *displaced* some distance "r" from that axis. It's length, a dimension perpendicular to the axis, is "a." I'm interested in finding the mass moment of inertia for the object. As I see it, I have two choices: (1) develop an integral describing the mass distribution of the object around the axis and then use the fundamental theorem and the interval r to r+a or; (2) use the parallel axis theorem, that is, develop definitive integrals describing both the mass distribution of the object at r=0 and around the axis at r->r+a, summing the two. So real simply, fundamental theorem or parallel axis theorem?

Thanks!

PTC
 
Physics news on Phys.org
I never really got my head round the parallel axis theorem, so I would use 1), which should be fairly easy, since the object is pointing straight away from the axis, it makes the integral fairly simple.
 
Thanks, Bruce! That's just about what I figured--it'd be much easier to compute over the interval. Thanks again!

PTC
 

Thread '1:1 versus 2:1 Mechanical Advantage debate'

The rope is tied into the person (the load of 200 pounds) and the rope goes up from the person to a fixed pulley and back down to his hands. He hauls the rope to suspend himself in the air. What is the mechanical advantage of the system? The person will indeed only have to lift half of his body weight (roughly 100 pounds) because he now lessened the load by that same amount. This APPEARS to be a 2:1 because he can hold himself with half the force, but my question is: is that mechanical...
View full post »

Thread 'Newton's first law?'

Some physics textbook writer told me that Newton's first law applies only on bodies that feel no interactions at all. He said that if a body is on rest or moves in constant velocity, there is no external force acting on it. But I have heard another form of the law that says the net force acting on a body must be zero. This means there is interactions involved after all. So which one is correct?
View full post »
Thread 'Beam on an inclined plane'

Thread 'Beam on an inclined plane'

Hello! I have a question regarding a beam on an inclined plane. I was considering a beam resting on two supports attached to an inclined plane. I was almost sure that the lower support must be more loaded. My imagination about this problem is shown in the picture below. Here is how I wrote the condition of equilibrium forces: $$ \begin{cases} F_{g\parallel}=F_{t1}+F_{t2}, \\ F_{g\perp}=F_{r1}+F_{r2} \end{cases}. $$ On the other hand...
View full post »

Similar threads

I Moment of inertia of human body with limbs at an angle
Replies
12
Views
2K
I Explanation of parallel axis theorem
Replies
2
Views
1K
I Resolve moment of inertia at an angle
Replies
2
Views
2K
How can I calculate the moment of inertia of any object?
Replies
10
Views
2K
Why Do Different Objects Share Similar Moments of Inertia?
Replies
1
Views
1K
Moment of inertia where mass and torque are at a different positions
2
Replies
69
Views
5K
Moment of inertia changes during rotation -- Calculate work?
Replies
3
Views
1K
1st, 2nd and mass moment of inertia
Replies
6
Views
5K
Moment of Inertia: Proving Mass, Side & Axis | 1/12 md²
Replies
3
Views
2K
Moment of inertia in plane translation
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top