- #1

HoodedFreak

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## Homework Statement

Two metal disks, one with radius R1 = 2.50 cm and

mass M1 = 0.80 kg and the other with radius R2 = 5.00 cm and

mass M2 = 1.60 kg, are welded together and mounted on a frictionless

axis through their common center, as in Problem 9.77.

(a) A light string is wrapped around the edge of the smaller disk,

and a 1.50-kg block is suspended from the free end of the string.

What is the magnitude of the downward acceleration of the block

after it is released? (b) Repeat the calculation of part (a), this time

with the string wrapped around the edge of the larger disk. In which

case is the acceleration of the block greater? Does your answer

make sense?

## Homework Equations

T = I * α

a = α * R

I of a cylinder = MR^2/2

T = F * l

## The Attempt at a Solution

a) The block is enacting a torque, which is equal to the force of gravity times the lever arm.

T = 1.5g * R

where R is the radius of the smaller cylinder

The moment of inertia of the system of cylinders is MR^2/2 for the smaller cylinder + (2M)*(2R)^2/2 for the bigger cylinder = 9MR^2/2

T = I*α ⇒ 1.5gR = 9MR^2/2 * α

3g = 9MR * α

3g = 9Ma

a = g/3M = 4.09 m/s^2

The answer however is a = 2.8

What did I do wrong?