Rotational Dynamics Help Needed

[lee_chick]

I'm sure there is something ridiculously simple I'm missing here but this questions has been driving me crazy and now I'm sure I couldn't see the answer if it stared me right in the face.

Homework Statement

A massless string is wrapped around a solid cylinder. A block of mass m=2.0kg hangs from the string. When released the block falls a distance of 82 cm in 2.0s. Starting with a freebody diagram calculate the mass of the cylinder.

*I can't use conservation of energy to solve this as the next question indicates that I am to solve the question again using conservation of mechanical energy.

Homework Equations

y = y₀ + v₀t + 1/2at²
F=ma
torsion = rF
Net Torsion = Moment of Inertia x rotational acceleration

The Attempt at a Solution

r = ? **This is the part that has me stumped - all of the formulae I know need a radius.
m = 2.0kg
y = 0.82m
t = 2.0s
v₀ = 0m/s
m_c = ?

Step One: Determine the force of inertia of the cylinder:

y = y₀ + v₀t + 1/2at²
a=(2y)/(t²)
a = (2 x 0.82m) / (2.0s²)
a = 0.41 m/s²
F_a = ma = 0.41m/s² x 2.0kg = 0.82N
F_g = mg = 9.81m/s² x 2.0kg = 19.62N
F_I = F_g - F_a = 19.62N - 0.82N = 18.8N


This is as far as I can get before I start running into brick walls. I've played with several different formulae but I always run into a point where I need the radius of the cylinder (which I don't have). Am I missing something really obvious here?

 

[Redbelly98]

Try solving it anyway, just leave the radius as "R" without plugging in a number for it. See what you can come up with that way.

p.s. Welcome to PF.