# Homework Help: Rotational Inertia, Need Help With Integrals

1. Apr 11, 2009

### rmunoz

Rotational Inertia, Need Help With Integrals!!!

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

In the figure below, a small disk of radius r = 2.00 cm has been glued to the edge of a larger disk of radius R = 4.00 cm so that the disks lie in the same plane. The disks can be rotated around a perpendicular axis through point O at the center of the larger disk. The disks both have a uniform density (mass per unit volume) of 1.50 103 kg/m3 and a uniform thickness of 4.60 mm. What is the rotational inertia of the two-disk assembly about the rotation axis through O?

http://www.webassign.net/halliday8e/art/images/halliday8019c10/image_n/nfg051.gif [Broken]

2. Relevant equations

I=$$\frac{MR\stackrel{2}{}}{2}$$

I=$$\int$$r$$\stackrel{2}{}$$dm

$$\rho$$= $$\frac{m}{v}$$

com= $$\frac{m1x1 + m2x2 + m3x3...m(n)x(n)}{M}$$

I=Icom + Mh$$\stackrel{2}{}$$

3. The attempt at a solution

My initial attempt basically included the following steps:

m(circle1)= $$\pi$$r1$$\stackrel{2}{}$$ * width [.0046m] * density [1.5*10$$\stackrel{3}{}$$kg/m$$\stackrel{3}{}$$]

m(circle2)= $$\pi$$r2$$\stackrel{2}{}$$ * width [.0046m] * density [1.5*10$$\stackrel{3}{}$$kg/m$$\stackrel{3}{}$$]

=> I(com)= $$\frac{1}{2}$$MR$$\stackrel{2}{}$$ Where R is the radius' of both circles added together

This clearly was the wrong approach and I'm fairly certain that in order to get the correct answer for this, i do not know how to take the integral (im only somewhat familiar with the process).

That integral is supposed to give me the I (com) and then im fairly certain all i have to do is find Mh^2 and add the two together to get the I (sys).

Would anybody mind helping me with this process, by explaining how to take a simple integral (preferably using these exact same terms), and what exactly this is doing for the calculations. This kind of assistance would be much appreciated!

Last edited by a moderator: May 4, 2017
2. Apr 11, 2009

### Staff: Mentor

Re: Rotational Inertia, Need Help With Integrals!!!

No integration is needed. Find the rotational inertia of each disk about point O, then add them for the total rotational inertia of the two-disk assembly. Hint: To find the rotational inertia of the smaller disk about point O, use the parallel axis theorem.

3. Apr 11, 2009

### rmunoz

Re: Rotational Inertia, Need Help With Integrals!!!

Got it, Thank you!