I'm trying to work out what the overall acceleration of an object in non circular uniform motion. My problem is thus, I am trying to model the time it would take an object to fall down the inside of an arc of a circle. I imagine it as a unit circle, with my object starting from rest at (-1,0) and finishing its journey at (0,-1). The radius of my circle is 30.2 m (actual lift hill height of a roller coaster in Ireland.) so far i have calculated the heights of both and velocity of both with final velocity being calculated by PCE: so 24.3294m/s. So far im having trouble resolving the time taken to complete this journey with gravity being 9.8m/s and friction and air resistance disregarded. Do I know enough variables to compute this? or is my issue elsewhere?
Asked
Active
Viewed 42 times
1
-
If I understand correctly, the system you are studying is a particle under the influence of gravity constrained to move on a circle? If so, it's equivalent to the pendulum: see https://physics.stackexchange.com/questions/653845/solution-to-pendulum-differential-equation?rq=1 It does not have a solution in terms of elementary functions, but depending on the initial conditions, and if you just want the time of a period, it might have a closed form. – Felipe Lopes Jan 22 '24 at 18:35
-
Yes thank you, I now understand it is a differential equation problem. Thank you. – David Jan 23 '24 at 19:22