Rotation Question: Masses on a Rotating Disk with Falling Block | Homework Help

[turbodan1]

Homework Statement

Three masses of 2kg, 2kg, and 4kg are attached to a massless disk of radius .1m. The disk rotates on a frictionless bearing through its center. A massless rope is wrapped around the outside of the disk. At the other end of the rope is a block of mass 8kg. As the block falls, the rope unwinds from the disk without slipping.

Homework Equations

1. Compute moment of inertia about the center of the disk for the system consisting of the disk plus attached masses.
2. The block is released from rest. Compute acceleration of the block.
3. Compute the tension on the rope as the block falls.

The Attempt at a Solution

1. I = mR^2
I = .01m^2 * 2kg + .01m^2 * 2kg + .01m^2 * 4kg = .08kgm^2
2. T = I a (lowercase a for angular acceleration)
Mg * R / I = a
8kg * 9.8m/s^2 * .1m / .08kgm^2 = 98rad/s
A (for linear acceleration) (pully) = A (Mass)
A(pully) = r * a
A = .1 * 99 = 9.8 m/s^2

Is this possible? Doesn't the non-zero I of the disk make the acceleration of the mass less than the acceleration due to gravity? Please let me know if my work is correct. If it's not, what did I do wrong?

Assuming this is correct, number 3 is 0N.

Thanks in advance

 

[kamerling]

If the block falls with acceleration b, it will only pull at the rope with a force M(g-b)