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Projectile Motion help required

  1. Apr 27, 2013 #1
    1. The problem statement, all variables and given/known data

    We need to find angular velocity of a particle from point of launch at its maximum height. Particle is launched at θ angle wrt horizontal. Initial velocity is u. Only acceleration is gravity.

    2. Relevant equations

    All projectile equations i suppose ( h(max)=u2sin2/2g , range= u2sin2θ/g etc) and of angular velocity ( v=ωXr)

    3. The attempt at a solution

    I suppose angular velocity is w° at initial. So, if i could get angular acceleration and then use ω=ω° + αt as at max height, i suppose angular velocity is 0 { same direction of both velocity and distance vectors, so θ = 0°}

    some help??
     
  2. jcsd
  3. Apr 27, 2013 #2

    cepheid

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    It seems easy enough to find θ vs. time given the trajectory, and then to say that ω = dθ/dt, assuming that you know what a derivative is.
     
  4. Apr 28, 2013 #3
    yes i know about derivative.

    but how do i plot that theta vs time graph??
     
  5. Apr 28, 2013 #4

    haruspex

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    That would assume the angular acceleration is constant, which it probably is not.
    What do you think the question means by angular velocity? It says "from the point of launch", so I think it means dθ/dt, where θ is the angle it subtends from its current position to the horizontal at the launch point. If so, it won't be zero at max height.
    Can you try writing its equations of motion in polar, origin at launch point?
     
  6. Apr 28, 2013 #5
    you mean that of trajectory??

    if yes, then i know that eqn. But what do i do with that equation??


    also forget what i attempted. i got it all wrong......

    also if i were to find angular acceleration as a function of sth, how would i do that??
     
    Last edited by a moderator: May 13, 2013
  7. Apr 28, 2013 #6

    haruspex

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    Then please post your working: equations of motion in Cartesian using the launch point as origin, then converted to polar form.
     
    Last edited by a moderator: May 13, 2013
  8. May 11, 2013 #7
    guys someone please help....

    a good person above asked me to post some equations but i have no idea which equations i need to post........


    if basic projectile equations are required, (that of range and velocity and max height, ) here they are


    range =[( u*sin {theta})^2]/2*g

    max height= [u^2 *sin[2*theta}]/g

    for velocity, we change the vertical component by eqn v=u-gt and take vector sum of horizontal and vertical components.....

    angular velocity : no idea

    angular acceleration : no idea.......
     
    Last edited by a moderator: May 13, 2013
  9. May 11, 2013 #8

    haruspex

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    By equations of trajectory, I mean the equations that tell you where the particle will be (x and y coordinates, say) at some time t after launch. I'm sure you know such equations, but you have not posted them yet.
     
  10. May 11, 2013 #9
    you mean this ?


    y= x*tan[theta] - (x^2)*g/(2*{u^2}*cos^2[theta])

    this is independent of time......

    in single directions, along horizontal direction s= u*cos{theta}*t

    along vertical direction s = u*sin[theta]*t - (g*t^2)/2
     
    Last edited by a moderator: May 13, 2013
  11. May 12, 2013 #10

    haruspex

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    Good, but to make it clearer, we'll write those as x=, y=...
    When at the point (x, y), what is the angle subtended to the horizontal at the launch point?
     
  12. May 13, 2013 #11
    i think arctan(y/x)
     
  13. May 16, 2013 #12
    any help??
     
  14. May 16, 2013 #13

    mukundpa

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    Can we calculate angular momentum of the particle about the launch point at the highest point? I think in that case to calculate the angular velocity will be easy.
     
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