# Acceleration of Two Disks Welded Together

1. The problem statement, all variables and given/known data

Two metal disks, one with radius R1 = 2.50 cm and mass M1 = 0.80 kg and the other with radius R2 = 0.500 cm and mass M2 = 1.60 kg, are welded together and mounted on a frictionless axis through their common center.

(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 has been released.

(I should add that there is a picture that looks like an axis going through a nickel and a dime stuck together, and there is a weight hanging from the string that is wrapped around the smaller disk.)

2. Relevant equations

τ = F*L = I(1)*α + I(2)*α, where L = radius, τ = torque and α = angular acceleration.

I = 0.5*M*R^2

a = α*L

3. The attempt at a solution

F*L = I(1)*α + I(2)*α

α = F*L/(I(1) + I(2))

α = (1.50kg *9.8*0.025m)/(0.5*0.8kg*(0.025m)^2 + 0.5*1.6kg*(0.05m)^2) = 163.333rad/s^2

a = α*L = (163.333rad/s^2)*0.025m = 4.08m/s^2