# How to understand the concept behind the rolling spool on a tabletop

1. Mar 25, 2013

### Ajith12

I have a problem involving the rotational version of Newton's Second Law. A spool is resting on a tabletop. A wire is wound around it counterclockwise and the free end of the wire goes over a pulley (located to the right of the spool) at the end of the table and attaches to a hanging mass. What happens to the spool when the system is released? Assume that there is friction between the spool and the table, and the spool undergoes pure rolling motion.

Does the spool roll away from/roll toward the pulley? If so, what happens to the hanging mass? Will it be at rest? or moving down, or moving up? If so, what is the reasoning behind it.
Thanks.

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2. Mar 25, 2013

### A.T.

What is the instantious point of rotation for a rolling spool? What is the moment from the thread force around that point?

Can the mass be at rest is the spool rolls? Can the mass move up without external energy input?

3. Mar 25, 2013

### rcgldr

Assuming this isn't homework, the spool rolls towards the hanging mass if the hub is smaller in radius than the spool, and away from the hanging mass if the hub is larger in radius than the spool (this would require that the spool be rolling on rails, with the larger radius hub free to rotate between the rails). If the hub has the same radius as the spool, then nothing moves unless the spool slides.

To confirm this, you can calculate what direction the wire moves if the spool rolls towards or away from the hanging mass (taking into account hub radius versus spool radius). The wire needs to move towards the hanging mass, since the only external force is gravity, which will accelerate the hanging mass downwards (unless nothing is moving).

Last edited: Mar 25, 2013