- #1

danielhep

- 14

- 1

## Homework Statement

A string is wrapped around a uniform solid cylinder of radius r, as shown in (Figure 1) . The cylinder can rotate freely about its axis. The loose end of the string is attached to a block. The block and cylinder each have mass m.

Find the magnitude α of the angular acceleration of the cylinder as the block descends.

## Homework Equations

F=ma=mg-T

Torque=Iα=-Tr

a=-rα

I=mr

^{2}/2

## The Attempt at a Solution

I use these three equations to eliminate T and solve for α.

m(-rα)=mg-T

-1/2mr=T

-mrα=mg+1/2mr

-α=g/r+1/2

α=-1/2-g/r

I tried this answer however it was wrong.

Mastering says the correct answer is

α = 2g/3r

I'm really not sure where this comes from, so any help would be great! I need to understand where I went wrong.