Moment of inertia by connecting two identical rods

[judas_priest]

Homework Statement

Four T-shaped objects are constructed by connecting two identical rods of equal mass and equal length. Rank in order, from LARGEST to SMALLEST, the moments of inertia for rotation about the axis indicated by the dashed line.

Homework Equations

The Attempt at a Solution

For the first, I used parallel axis theorem for the rod length l away, and for the rod perpendicular to the axis, I took its MI as m*l^2/3. I'm pretty sure that's a wrong approach. I need someone to point out how to go about this.

 

[voko]

You do not really need to compute the moments. You can use the general formula and compare them by reasoning whether terms in the formula will be larger or smaller.

 

[Chestermiller]

Homework Statement

Four T-shaped objects are constructed by connecting two identical rods of equal mass and equal length. Rank in order, from LARGEST to SMALLEST, the moments of inertia for rotation about the axis indicated by the dashed line.

Homework Equations

The Attempt at a Solution

For the first, I used parallel axis theorem for the rod length l away, and for the rod perpendicular to the axis, I took its MI as m*l^2/3. I'm pretty sure that's a wrong approach. I need someone to point out how to go about this.

Try this. Just look at the pictures. Which do you think has the largest moment of inertia, and which do you think has the smallest? Compare the two intermediate cases. Which do you think has the larger and which do you think has the smaller?

Chet

 

[judas_priest]

Try this. Just look at the pictures. Which do you think has the largest moment of inertia, and which do you think has the smallest? Compare the two intermediate cases. Which do you think has the larger and which do you think has the smaller?

Chet

A has the largest and C the smallest? Only using intuition and a little physics. Please correct if I'm wrong.

 

[judas_priest]

You do not really need to compute the moments. You can use the general formula and compare them by reasoning whether terms in the formula will be larger or smaller.

In that case A=D. Correct?

 

[voko]

Cases A and D is similar. The total moment in both case is the sum of the moment of the bar perpendicular to the axis of rotation, and of the moment of the bar parallel to the axis. The moment of the perp. bar is the same in both case; but is the moment of the par. bar the same? Observe its distance from the axis is not equal in the two cases.

 

[judas_priest]

Cases A and D is similar. The total moment in both case is the sum of the moment of the bar perpendicular to the axis of rotation, and of the moment of the bar parallel to the axis. The moment of the perp. bar is the same in both case; but is the moment of the par. bar the same? Observe its distance from the axis is not equal in the two cases.

How do I find the perpendicular Moment of inertia?

 

[voko]

How do I find the perpendicular Moment of inertia?

Well, any moment of inertia is "perpendicular" in the sense that you consider the distance from the axis of rotation, and the distance is perpendicular to the axis.

But what really meant was that there two bars, one in perpendicular and the other parallel to the axis of rotation, and they have certain moment about the axis.

 

[judas_priest]

Well, any moment of inertia is "perpendicular" in the sense that you consider the distance from the axis of rotation, and the distance is perpendicular to the axis.

But what really meant was that there two bars, one in perpendicular and the other parallel to the axis of rotation, and they have certain moment about the axis.

Let me reframe my question -
How do I find the the moment of inertia of the rod perpendicular to the axis asked to find about

 

[voko]

Like I said, you do not really need to find it in this problem. But if you want to anyway, you need to use the general formula for the moment of inertia.

 

[judas_priest]

Like I said, you do not really need to find it in this problem. But if you want to anyway, you need to use the general formula for the moment of inertia.

How do I find the moment of inertias in this case? Which is greater than which?

 

[voko]

How do I find the moment of inertias in this case? Which is greater than which?

I do not know what "this case" is.

Anyway, what is the definition of the moment of inertia?

 

[judas_priest]

I do not know what "this case" is.

Anyway, what is the definition of the moment of inertia?

This case being the question I posted to start the thread. Moment of inertia gives a general idea of the distribution of mass. Given by I = M*R^2

 

[voko]

I have already suggested how you could handle this problem, with more details given in #6. I do not think you hear what I have been saying.

 

[Chestermiller]

A has the largest and C the smallest? Only using intuition and a little physics. Please correct if I'm wrong.

These are both correct. Now all you need to do is to decide between B and D. Note that the portion of the "T" perpendicular to the axis of B is the same as the portion of the "T" perpendicular to the axis of D. How do the portions of the T's parallel to the axes in this two figures compare in terms of their distances from the axis?