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1. a cylinder rolls on a smooth surface without slipping; its top is connected to a spring which is fixed at one end. show that if the cylinder's centre of mass is displaced by a distance u, the spring is displaced by 2u.
2. (Original post by idunnowhattoputhere)
a cylinder rolls on a smooth surface without slipping; its top is connected to a spring which is fixed at one end. show that if the cylinder's centre of mass is displaced by a distance u, the spring is displaced by 2u.
What is the moment of inertia for the cylinder? And also, it says "without slipping". What is the significance of this?

Hint:
Spoiler:
Show
Consider the equation v = rw. If you differentiate it w.r.t. t, what do you get? This is the case when there is no slipping occurring.
3. (Original post by Mathematician!)
What is the moment of inertia for the cylinder? And also, it says "without slipping". What is the significance of this?

Hint:
Spoiler:
Show
Consider the equation v = rw. If you differentiate it w.r.t. t, what do you get? This is the case when there is no slipping occurring.
sorry, i can do all of that but i'm still struggling to see how it solves the problem.
4. solved. for anyone interested, consider the total energy (kinetic and rotational) of the system then differentiate (you will have to use the chain rule twice). you should end up with x (lateral movement) = -0.5aS, where S = 'theta' and 'a' is the radius (and so aS is the arc-length), after you are done with the algebra.
5. (Original post by idunnowhattoputhere)
solved. for anyone interested, consider the total energy (kinetic and rotational) of the system then differentiate (you will have to use the chain rule twice). you should end up with x (lateral movement) = -0.5aS, where S = 'theta' and 'a' is the radius (and so aS is the arc-length), after you are done with the algebra.
Gah, completely forgot to come back to explain the rest!
Anyway, well done for solving it.

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