Torque on a Cylinder

  • #1
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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: F1 = 5.0 N, F2 = 6.0 N, F3 = 2.5 N, and F4 = 5.5 N. Also, R1 = 6.5 cm and R2 = 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.)

phys fig.jpg


Homework Equations


τ=I⋅α=r⋅F⋅sinΦ
Icyl = ½MR2

The Attempt at a Solution


So I started with
τnet=F2⋅R1 - F1⋅R2 + F4⋅0
and τ=Iα , so F2+R1 - F1⋅R2=Iα.
Substituting in I:
F2⋅R1 - F1⋅R2=½MR2α
Solved for α to get
2[F2⋅R1 - F1⋅R2 ]/MR2
Plugging and chugging I got:
2[(6.0N-5.0N)(0.12m)+(2.5N)(0.065m)]/(5.0kg)(0.12m)2
α=0.94 rad/s2

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

Answers and Replies

  • #2
686
172
I didn't work all the way through your solution (I don't have much time right now), but your original τnet equation has errors. You should carefully go through that.
 

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