Torque and Forces in Spool Movement: Solving for Net Torque and Static Friction

[jaewonjung]

Homework Statement

Problem in picture

Relevant Equations

Fnet=ma

Forces in the x direction: static friction left=Tcostheta to the right
Forces in the y direction: W= Normal force + Tsintheta
Net torque: rTcostheta-RFs=0

Fs=Tcostheta,
rTcostheta-R(Tcostheta)=0
rTcostheta=RTcostheta
r=R

Please help

 

[hutchphd]

This is a multiple choice question, so try to use intuition about rolling vs slipping to eliminate answers. Look at each variable in turn: for instance what if r=R? Will it roll? Then think about theta...what if it is zero...90deg...

 

[haruspex]

Net torque: rTcostheta-RFs=0

Looks like you are taking moments about the centre of the cylinder. Think again about the torque due to T. Maybe draw a nice big picture, carefully.
(There is a better choice of axis for this problem.)

 

[jaewonjung]

I solved it! The torque of the Tension is just Tr, not Trcostheta. Thanks for the help!

 

[haruspex]

I solved it! The torque of the Tension is just Tr, not Trcostheta. Thanks for the help!

Good.
Note that if you take moments about the point of contact with the ground instead it becomes a matter of simple geometry.