Rotacny a translacny pohyb ocelovej gule na lanku


Predstavme si disk s polomerom a vertikalnou osou upevnenou na voziku. Pri pohlade zhora bod opisuje cykloidu ked konstatna obvodova rychlost sa rovna konstantnej rychlosti vozika a pricom je konstantna uhlova rychlost. Zobrazene na nasledovnom obrazku:

Steel ball box

Na bod posobi odstrediva sila/zrychlenie , dostrediva sila/zrychlenie a tangencialna sila/zrychlenie .
Vyslednu silu/zrychlenie dostaneme suctom a , ktore smeruje do stredu disku.

Teraz polozme a pripevnime ocelovu gulu na disk v bode , ktora je ocelovym lankom pripojena na os .

Steel ball box

The ball is brought up to constant angular velocity by some convenient means, for example the ball would be physically attached to the disk and it would be detached from the disk once we reach ideal cycloid trajectory. Assuming a frictionless situation, the steel ball will remain in orbit forever, as a moon in orbit around a planet. In this situation, the ball still feels centrifugal acceleration due to its inertia. There is a tension force on the string always in the radial direction to the axis , otherwise the ball would fly off.

But what about the third acceleration, ? How large is it compared to the disk case and in what direction?

Steel ball box

The end result effect of the will be the steel ball acceleration.
The steel ball will speed up and the cycloid will become more prolate.

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