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Calculating minimum velocity around a loop

  1. Oct 2, 2015 #1
    So I had this question for physics about something going around a loop. The question asked what the minimum velocity to counteract gravity is if something is going around a loop. hint: One force will be zero.

    I'm not sure how to figure this out, can someone help?
     
  2. jcsd
  3. Oct 2, 2015 #2

    Mentallic

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    Can you calculate the centripetal acceleration of a particle moving at some velocity around the loop? You can assume the loop is of radius r and treat it as a constant.
     
  4. Oct 3, 2015 #3

    HallsofIvy

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    If an object is going around a loop of radius R at constant angular velocity, [itex]\omega[/itex] then its position vector (taking center of the loop to be (0, 0) and the objects position at t= 0 to be (1, 0)) is [itex]R cos(\omega t)\vec{i}+ R sin(\omega t)\vec{j}[/itex]. Its velocity vector will be [itex]-\omega R sin(\omega t)\vec{i}+ \omega R cos(\omega t)\vec{j}[/itex] and its acceleration vector will be [itex]-\omega^2 R cos(\omega t)\vec{i}- \omega^2 R sin(\omega t)\vec{j}[/itex]. In order to stay on the loop, the acceleration at the top ([itex]\theta= \pi/4[/itex]) must be non-negative.
     
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