Rotational Inertia of Disk2: 16I or 8I?

[The_Journey]

Homework Statement

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.

Homework Equations

I = m * r ^ 2
Density = Mass / Area

The Attempt at a Solution

I tried using density because the two disks are uniform so their densities must equal. But I don't 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?

 

[ehild]

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

ehild

 

[The_Journey]

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