# Man on the platform

1. Feb 5, 2016

### bznm

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. Feb 5, 2016

### J Hann

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?

3. Feb 5, 2016

### haruspex

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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