# Opening a bottle cap

How exactly is a bottle cap opened/closed? To open/close one, it needs to be rotated and simultaneously translated upwards/downwards for it to move up/down its thread and not be translated right or left alongside.

From my understanding, for this, I’d need to apply an equal and opposite force so the cap doesn’t slide right or left and provide torque for it to rotate. How does this make it move up/down? It must be because of the thread somehow but how exactly?

And for an equal and opposite force, I need to use two fingers, how can I be so precise so as to apply equal and opposite forces with my fingers? And how is it possible to open/close a cap with one finger then? Then I’d have no equal and opposite force and the cap should translate right or left? Does it being constrained to the bottle neck prevent that? So the bottle neck applies a normal equal and opposite to the force my finger applies and that prevents sliding right or left?

(I’m new to this, my notions are probably wrong or very basic.)

1. How does this make it move up/down?

Yes it is the thread as you suspect. The motion caused by your fingers makes the thread of the cap push against that of the bottle. There results a normal reaction force between the two threads, and the direction is such as to move the cap up and the bottle down (when unscrewing, with bottle vertically oriented in the normal way).

1. How can I be so precise?

This is to do with feedback. You provide some sort of combination of forces. If one side of the cap gets a larger force than the other, then the cap will begin to accelerate in the direction of the unbalanced force. Your hand holding the bottle, or a stand if the bottle is fixed in some way, then acts to prevent this acceleration, building up its force until there is just the right balance. If you are using your hand then your eyes and brain contribute to determining when the balance has been reached. If the bottle is fixed in some stand then the stand simply does not move (being attached to Earth or something) so the forces build up to whatever is required to prevent motion of the bottle relative to the stand.

1. How is it possible to open with one finger?

Like part two, there are other forces also acting on the bottle; these provide the other part which prevents the bottle from accelerating as a whole.

1. What about the forces exerted by the cap on my fingers?

The forces exerted by the cap/bottle on your fingers do not affect the motion of the bottle; they affect the motion of your fingers. Your hand and wrist provide further forces on your fingers. Your fingers accelerate in response to the combination of the forces acting on them.