# Hoop with seven spokes finding Inertia

1. May 30, 2009

### physics10189

1. The problem statement, all variables and given/known data
A wheel is formed from a hoop of mass 2.2kg and seven equally spaced spokes, each of mass 0.13kg. The hoop's radius is the length 0.54m of each spoke.

Find the moment of inertial of the whell about an axis through its center and perpendiucular to the plane of the wheel.

2. Relevant equations

3. The attempt at a solution
So I use the inertia of the hoops
I=Mr^2
so there are seven radius
M=(7*.13)+2.2
R=(.54)
which i get .906876
I am doing something, right?

2. May 30, 2009

### rock.freak667

the spokes are rods of length .54m

3. May 30, 2009

### D H

Staff Emeritus
Something, but not everything. What is the moment of inertia for a rod of mass m and length l rotating about an axis normal to the rod, with the axis of rotation at the end of the rod?

4. May 30, 2009

### physics10189

Oh wow i never thought about rod, but I think it is unneccessary for the rod to have an inertia because it never define the spokes are rods.
But I would like to here your advice how would i combine the inertia of the hoop and the rod
Inertia of rod is (1/12)ML^2

5. May 30, 2009

### Ilivian

Well, because one top of the the rod is at the center of the wheel, u should easily find its moment of inertial. Then just time 7.

Find the hoop's moment of inertial, plus all together.

6. May 30, 2009

### D H

Staff Emeritus
Not in this case.

7. May 30, 2009

### physics10189

Well I assume the inertia of the rod is (1/12)(7*M)(L^2)
right?

8. May 31, 2009

### D H

Staff Emeritus
No. Repeating from post #3, what is the moment of inertia for a rod of mass m and length l rotating about an axis normal to the rod, with the axis of rotation at the end of the rod?

9. May 31, 2009

### physics10189

Ok i understand, I saw my mistake.

Here is another problem
Determine the moment of inertia of teh wheel about an axis through its rim and perpendicular to the plane of the wheel.

Does this mean that the wheel is now on the axis? or something else?

10. May 31, 2009

### LowlyPion

This means they want you to apply the || axis theorem to the moment of inertia for the wheel about its center doesn't it?

11. May 31, 2009

### physics10189

I do not know what you mean by that.

12. May 31, 2009

### D H

Staff Emeritus
Two vertical lines || is short for parallel. You need to use the parallel axis theorem.

13. May 31, 2009

### physics10189

Ok so I found the parallel axis theorem
I=Icm+MD^2

the only problem is what is going the be the Icm
Is it the sum of 7 spokes and the hoop
also is the M the total mass of the 7 spokes and the hoop
and what is D
is D just the radius?

14. May 31, 2009

### LowlyPion

What they want you to do is use find the moment of inertia. So yes it is the moment of 7 spokes plus the rim. That is the Icm.

That done then apply the (|| sorry for that) parallel axis theorem, which would be using the total Mass and the displacement, which in this case is the Radius L.