A uniform hoop is supported so it hangs in the vertical plane by a knife edge. Set into oscillation in the plane, this physical pendulum has a natural period of oscillation. Subsequently, symmetric sections starting from the bottom of the hoop are cut off. What is the period of the half hoop? Of a quarter hoop? What is the surprise in the behavior of this oscillating system?

Question

irishboy123 · Answer

i am v sure that, if you can dig out the moment of inertia/ centre of mass stuff for a ring about a point on it's radius, you can merrily plug into the basic shm DE: $\ddot \theta + \omega^2 \theta = 0$ and draw some kinda  conclusion.....

...which might be "surprising"  :-)


are you stuck at some particular point?!  looks laborious.

irishboy123 · Answer

and BTW, the knife-edge part of the qu makes it wrong IMHO

as soon as the ring is given some kinda nudge, it has to slip.  so it should be on some kinda hinge for this to work.  i'd say.

basicallyautumn · Answer

@IrishBoy123 thank you!