A small button placed on a horizontal rotating platform withdiameter 0.300 m wil

Question

A small button placed on a horizontal rotating platform withdiameter 0.300 m will revolve with the platform when it is broughtup to a speed of 30.0 rev/min, provided the button is no more than0.120 m from the axis. (a) What is the coefficient of static frictionbetween the button and the platform?
1.       ?

(b) How far from the axis can the button be placed, withoutslipping, if the platform rotates at 45.0 rev/min?
2.       ? m (a) What is the coefficient of static frictionbetween the button and the platform?
1.       ?

(b) How far from the axis can the button be placed, withoutslipping, if the platform rotates at 45.0 rev/min?
2.       ? m

Explanation / Answer

   The button will start slipping when thecentrifugal force exceeds the force of static friction i.e.     * m *g   =   m * r * 2       =   r* 2 / g    r   =   radiusof button       =   angularspeed    a.   r   =   0.120   m             =   30.0   rev/min                =   30.0* 2 / 60                =   3.14   rad/s             =   0.120* 3.142 / 9.8                =   0.121       =   r* 2 / g    r   =   radiusof button       =   angularspeed    a.   r   =   0.120   m             =   30.0   rev/min                =   30.0* 2 / 60                =   3.14   rad/s             =   0.120* 3.142 / 9.8                =   0.121    b.   let the distace fromaxis be 'd'.          =   45rev/min             =   45* 2 / 60             =   4.71   rad/s       0.121   =   d* 4.712 / 9.8          d   =   0.121* 9.8 / 22.184             =   0.0534   m

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