# Homework Help: Find the rotational inertia of the assembly. (Rod and Particles)

1. Apr 1, 2010

### Wm_Davies

1. The problem statement, all variables and given/known data[/b]

I need help with part (a) of this problem. (See attachment)

In Fig. 11-45, three particles of mass m = 3.9 kg are fastened to three rods of length d = 0.40 m and negligible mass. The rigid assembly rotates about point O at angular speed ω = 9.1 rad/s. About O, what are (a) the rotational inertia of the assembly, (b) the magnitude of the angular momentum of the middle particle, and (c) the magnitude of the angular momentum of the assembly?

2. Relevant equations

Rotational Inertia for a rod = $$\frac{1}{12}(ML^{2})$$
Rotational Inertia for a Particle = mr^2 (Where r is the distance from the point of rotation)

3. The attempt at a solution

First I took the three rods and made them into one long one with three particles attached to it and used the parallel axis theorem to adjust the rotational inertia for the rod.

Which gave me the equation of......

$$\frac{1}{12}[ML^{2}+ML^{2}]+m[(r)^{2}+(2r)^{2}+(3r)^{2}]=I$$

I substitute in the notation used in the problem and remove the M for the rod since it is negligible.

$$\frac{1}{12}[(3d)^{2}+(1.5d)^{2}]+m[(d)^{2}+(2d)^{2}+(3d)^{2}]=I$$

After plugging in the numbers for this I had gotten.....

$$\frac{1}{12}[(3*.3)^{2}+(1.5*.3)^{2}]+4.2[(.3)^{2}+(2*.3)^{2}+(3*.3)^{2}]=I$$

Which gave me the result of....
5.37638 kg*m^2

Which is not correct, but I cannot see what I did wrong. I would appreciate any help. I know that the correct answer is 5.292 kg*m^2

#### Attached Files:

• ###### fig11_43.gif
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Last edited: Apr 1, 2010
2. Apr 1, 2010

### Wm_Davies

I found that since the mass of the rod is negligible it is actually equal to zero which eliminates any rotational inertia for the rod. I also had the equation wrong for the horizontal shift of the axis, but that didn't factor into the problem I was having.

3. Apr 1, 2010

### Staff: Mentor

The rod pieces are massless, so they contribute nothing to the rotational inertia. (When you 'removed' the mass of the rod, you just erased it! Instead, set M = 0.)