1
$\begingroup$

I have a conceptual question about the problem, I'm not requesting a solution. I just don't know how to implement the condition of the full swing. I know that the tension at the top is zero. But if I get the velocity from there, how does that help me? I know the velocity of the object at the top of the circle. How does that ensure that it makes a full circle? How do I know that it won't fall off after a while before completing a circle?

$\endgroup$
3
  • $\begingroup$ The solution depends on how the pendulum is realized/defined. Either a mass moving along a circle (constraint of fixed distance from the rotation center, implemented, for instance, with a massless rod) or a mass attached to a flexible wire. $\endgroup$ Jan 8, 2023 at 16:23
  • 1
    $\begingroup$ @GiorgioP it's a simple pendulum. A bob on a massless inextensible string. $\endgroup$
    – EM_1
    Jan 8, 2023 at 16:33
  • $\begingroup$ How does that ensure that it makes a full circle? How do I know that it won't fall off after a while before completing a circle? Simple penduli don't complete full circles. $\endgroup$
    – Gert
    Jan 8, 2023 at 16:40

1 Answer 1

0
$\begingroup$

At any point lower than the top of the circle, the velocity will be higher (because of energy conservation, and the acceleration in the direction perpendicular to the circle due to gravity will be smaller. This means that having enough velocity on the top of the circle (so that in the next moment the particle will still be attached to it) imply that you will also have enough velocity at any lower point to do so.

$\endgroup$
2
  • 1
    $\begingroup$ I don't fully understand your answer, but I understand that the velocity will be a minimum at the top. How does that guarantee that the pendulum will make a complete circle while the string is still taut? $\endgroup$
    – EM_1
    Jan 8, 2023 at 17:43
  • $\begingroup$ In order for the string to be not tenced you should have a moment in which the radial veocity of the ball at the end will vanish and that its accalaration will be inward (to the center) - otherwise it will imiddietly get tenced in the next moment). At the top the radial velicty is indeed vanish by your conditon but the accelaration is 0 . Then it follow from my answer that it also won't happand at any other moment. $\endgroup$
    – ziv
    Jan 8, 2023 at 18:03

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.