# Seriously stumped by rotational motion

i havent really been following the solution process to this thread very closely so i may have missed the answer to my question, but what units do you yanks use in order to differentiate between mass and weight? we use kilograms for mass and newtons for the weight, but i noticed you used lbs all over the place.

The cylinder and box are both 0.25 slug. I have no idea why it's called a slug.

I think this is the solution, but I'm not a physicist.
I won't use specific numbers since I'm not sure if e.g.
your 8 lbs. is a force or is used as a mass instead of slugs.

Let:

M = mass of cylinder
I = moment of inertia of cylinder = (MR^2)/2
a = translational acceleration of cylinder and block
A = rotational acceleration of cylinder
T = tension in string
m = mass of block
e = coefficient of friction of block
f = frictional force on block = em
g = acceleration of gravity

We have the following relationships:

Mg - T = Ma (eqn 1)
T - f = ma (eqn 2)

from the rotational motion:

TR = IA and A = a/R since the only force that causes
rotation is the tension

then TR = ((MR^2)/2)(a/R) = MRa/2
and T = Ma/2 (eqn. 3)

Substituting eqn 3 in eqn 1 we get:

a = 2g/3 and so T = Mg/3 after substituting back into eqn 3

However from substituting in eqn 2 it must also be true that

a = (2m/(M-2m))e

Unfortunately, PTKarch's solution is similar to my incorrect solution on page 1. Worse really, since it tries to use the same "a" for the block and the cylinder (which DON'T accelerate at the same rate).

Anyway, the correct solution is posted above -- the one headed with "woops" at the middle of page 2.