# Homework Help: Rotational Dynamics Help Needed

1. Oct 20, 2008

### 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.

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

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.

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

3. 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
mc = ?

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
Fa = ma = 0.41m/s2 x 2.0kg = 0.82N
Fg = mg = 9.81m/s2 x 2.0kg = 19.62N
FI = Fg - Fa = 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?

2. Oct 20, 2008

### Redbelly98

Staff Emeritus
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.