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

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The discussion revolves around a physics problem involving three masses attached to a rotating disk and an 8kg block that falls, unwinding a rope. The moment of inertia for the system was calculated as 0.08 kgm². The acceleration of the falling block was derived, leading to a linear acceleration of 9.8 m/s², raising concerns about whether this value is feasible given the disk's moment of inertia. The user questions if the non-zero moment of inertia affects the block's acceleration, suggesting that the acceleration should be less than gravity. The final tension in the rope was stated as 0N, indicating a misunderstanding of the forces at play.
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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
 
Physics news on Phys.org
If the block falls with acceleration b, it will only pull at the rope with a force M(g-b)
 

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