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## Homework Statement

A cylinder having a mass of 5.0

*kg*can rotate about its central axis through point O. Forces are applied as shown in the figure: F

_{1}= 5.0

*N*, F

_{2}= 6.0

*N*, F

_{3}= 2.5

*N*, and F

_{4}= 5.5

*N*. Also, R

_{1}= 6.5

*cm*and R

_{2}= 12.0

*cm*. Find the magnitude and direction of the angular acceleration of the cylinder. (Take clockwise to be +.) (During the rotation, the forces maintain their same angles relative to the cylinder.)

## Homework Equations

τ=I⋅α=r⋅F⋅sinΦ

I

_{cyl}= ½MR

^{2}

## The Attempt at a Solution

So I started with

τ

_{net}=F

_{2}⋅R

_{1}- F

_{1}⋅R

_{2}+ F

_{4}⋅0

and τ=Iα , so F

_{2}+R

_{1}- F

_{1}⋅R

_{2}=Iα.

Substituting in I:

F

_{2}⋅R

_{1}- F

_{1}⋅R

_{2}=½MR

^{2}α

Solved for α to get

2[F

_{2}⋅R

_{1}- F

_{1}⋅R

_{2}]/MR

^{2}=α

Plugging and chugging I got:

2[(6.0N-5.0N)(0.12m)+(2.5N)(0.065m)]/(5.0kg)(0.12m)

^{2}=α

α=0.94 rad/s

^{2}

But this isn't correct. Can you help me figure out what I'm doing wrong? Thanks!