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    I have a bead on a wire that is at an angle to the vertical, I need to show that there is a starting distance along the wire where the bead will exhibit circular motion regardless of the radius.

    Working in spherical polars I get the equation of motion as

    mr''=mr(wsin(a))^2-mgcos(a)

    which yields

    r=A(e^wsin(a)t)-B(e^-wsin(a)t)+(gcos(a)/(wsin(a))^2)

    I have been asked to show that for r0=gcos(a)/(wsin(a)) the particle exhibits circular motion. However, I get a hyperbolic function - which is correct for other starting conditions... and can't show that r'=0...

    Any help appreciated. Thanks.
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    (Original post by natninja)
    I have a bead on a wire that is at an angle to the vertical, I need to show that there is a starting distance along the wire where the bead will exhibit circular motion regardless of the radius.

    Working in spherical polars I get the equation of motion as

    mr''=mr(wsin(a))^2-mgcos(a)

    which yields

    r=A(e^wsin(a)t)-B(e^-wsin(a)t)+(gcos(a)/(wsin(a))^2)

    I have been asked to show that for r0=gcos(a)/(wsin(a)) the particle exhibits circular motion. However, I get a hyperbolic function - which is correct for other starting conditions... and can't show that r'=0...

    Any help appreciated. Thanks.
    could you post the full question please? it's not clear to me what you mean/what the variables are.
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    (Original post by ben-smith)
    could you post the full question please? it's not clear to me what you mean/what the variables are.
    question 7b, think question is wrong and should be sin squared rather than sin as it works then.

    EDIT attachment failed...
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    (Original post by ben-smith)
    could you post the full question please? it's not clear to me what you mean/what the variables are.
    here?
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    (Original post by natninja)
    here?
    you are pretty much there. note that they gave you initial conditions.
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    (Original post by ben-smith)
    you are pretty much there. note that they gave you initial conditions.
    solved it - question was wrong... now stuck on 3c...
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    (Original post by natninja)
    solved it - question was wrong... now stuck on 3c...
    The trick is to notice that the second system is not inertial so you have to modify N2 when treating it.
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    (Original post by ben-smith)
    The trick is to notice that the second system is not inertial so you have to modify N2 when treating it.
    yeah got that didn't notice that T1=2T2 which made it come out in a few lines... but thanks

    Though there is no way I can work out the potential function in 8b - using Divergence theorem maybe?
 
 
 
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