- #1

songoku

- 2,340

- 340

- Homework Statement
- I am trying to solve question in this link:

https://www.chegg.com/homework-help/spool-thread-mass-m-rests-plane-inclined-angle-end-thread-t-chapter-8-problem-108cp-solution-9780077405731-exc

- Relevant Equations
- torque = F x d

torque = I . α

Newton's law

friction = μ . N

a) Describe the motion of the spool: it will roll down the plane, rotating counter clockwise.

I am confused when setting up equation of torque. If I take center of the spool as pivot, only the tension of thread produces torque but the direction will be clockwise and it makes the spool will move upwards instead of downwards.

If I take the bottom point of the spool that is in contact with the plane as the pivot, there will be two forces producing torque: tension and weight. The equation will be:

mg sin θ . R - T .(R + r) = I . α

mg sin θ . R - T .(R + r) = I . a / R (where a is the acceleration of the center of mass of the spool). Is this equation correct?

If yes, why taking different pivot will give different equations? I think no matter where I put the pivot, the equation should be the same?

b) direction of frictional force: upwards parallel to the plane (in the same direction as tension). Is this correct?

Thanks

I am confused when setting up equation of torque. If I take center of the spool as pivot, only the tension of thread produces torque but the direction will be clockwise and it makes the spool will move upwards instead of downwards.

If I take the bottom point of the spool that is in contact with the plane as the pivot, there will be two forces producing torque: tension and weight. The equation will be:

mg sin θ . R - T .(R + r) = I . α

mg sin θ . R - T .(R + r) = I . a / R (where a is the acceleration of the center of mass of the spool). Is this equation correct?

If yes, why taking different pivot will give different equations? I think no matter where I put the pivot, the equation should be the same?

b) direction of frictional force: upwards parallel to the plane (in the same direction as tension). Is this correct?

Thanks