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Man on the platform

  1. Feb 5, 2016 #1
    1. The problem statement, all variables and given/known data
    A platform rotates in counterclockwise with angular velocity w.
    A man walks frm the center of the platform to the border with constant radial velocity v' wrt the platform.
    ##\mu_s## is the static friction coefficient.

    Calculate the minimum value for ##\mu_s## such that the radial motion is straight.
    What about a', value of the man acceleration wrt the platform?

    2. Relevant equations
    ##a_0=a'+a_{cc}+a_c##

    where ##a_0## absolute acceleration, a'=man acceleration wrt the patform, ##a_{cc}= 2 w x v'##, ##a_c=-w^2 r u_r##

    ##u_r##= unit vector with radial direction
    ##u_t##= unit vector with tangent direction

    3. The attempt at a solution
    absolute velocity : ##v_0=v' u_r+wr w_t##
    absolute acceleration: ##dv_0/dt=2v' w u_t-w^2r u_r##

    I want that the man goes straight on respect with an observer on the paltform, so I "cancel" the Coriolis acceleration:
    ##\mu_s =2v'w/g##

    ##a'=a_0-a_{cc}-a_c+a_{friction}=2v'wu_t##

    But I have obtained the Coriolis acceleration! ... Something went wrong. Please, help me!
     
  2. jcsd
  3. Feb 5, 2016 #2
    Doesn't the man experience a "fictitious" force which is the Coriolis force?
    What happens if you look at the problem from the actual inertial frame?
    Then the angular momentum is I w (where w is the angular velocity).
    What is the torque required to produce the change in angular momentum due to
    the man walking on the platform?
     
  4. Feb 5, 2016 #3

    haruspex

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    Agreed, if you mean that vectorially. And you know a', yes? So what is the net acceleration?
    No, that assumes the only acceleration of the man is Coriolis. There is also centripetal/centrifugal.
     
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