- #1

hadsox

- 1

- 0

## Homework Statement

A uniform spool of mass M and diameter d rests on end on a frictionless table. A massless string wrapped around the spool is attached to a weight m which hangs over the edge of the table. If the spool is released from rest when its center of mass is a distance l from the edge of the table, what is the velocity of the weight m when the center of mass of the spool reaches the edge of the table?

## Homework Equations

## The Attempt at a Solution

My attempt:

I thought of breaking up the problem into two cases and the combining them at the end.

case1: Pretend no rotation:

With no rotation the spool has forces Tension acting on it. T = Ma

The mass attached to the string has forces Tension and gravity. solved for T' = mg - ma

Since the acceleration for both we can get to [a = (mg)/(M+m)

So, we can get a final velocity of v = √(2*(mg)/(M+m)*l). where I started with v

_{f}

^{2}= v

_{i}

^{2}+2*a*l, l being the displacement of the spool on the table.

Case2: Pretend no translation:

With no translation, I believe then the Tension and Torque are equal to each other. Then we can get α = (τ/I). and we can get θ = l/(π*d),

What I end up using is the angular kinematics to get ω

_{f}= √(2*(τ/I)*(l/(π*d))

So this is my work...am I on the rigth track or completely wrong? And how can I relate these two to get a uniform equation?