# Rotational Inertia.

1. Feb 23, 2010

### The_Journey

1. The problem statement, all variables and given/known data
There are two uniform disks. Disk 1 has radius of R, a rotational inertia of I. Disk 2 has radius of 2R, what is the rotational inertia of Disk2 in term of I? The disks are rotating about their center axis.

2. Relevant equations
I = m * r ^ 2
Density = Mass / Area

3. The attempt at a solution

I tried using density because the two disks are uniform so their densities must equal. But I dont have the mass for both of the disks so I just call mass of Disk1 to be M. So Disk1 density is:
M / (pi * R^2). Setting it equal to xM / (4 * pi * R ^ 2) and solve for x.

So mass of Disk2 is 4M, which is 4 times the mass of Disk1. I is the rotational inertia of Disk1 so it must be this:

I = (1/2) * M * R ^ 2.

Then the rotational inertia of Disk2, which has Radius of 2R and mass of 4M is:

I2 = (1/2) * (4M) * (2R)^2 = 8 * M * R ^ 2.

Dividing I2 by I gets me 16.

So the answer I think is 16I, the rotational inertia of Disk2 is 16 times the rotational inertia of Disk1, but this seems too high and my friend got 8I, so can anyone show me the correct way?

2. Feb 23, 2010

### ehild

Your result is correct. Why do you think it is high?

ehild

3. Feb 23, 2010

### The_Journey

I guess doubling the radius gets you 16 times the rotational inertia seems kinda crazy. Anyway thank you for verifying