A circular platform of radius Rp = 4.51 m and mass Mp = 327 kg rotates on fricti

Question

A circular platform of radius Rp = 4.51 m and mass Mp = 327 kg rotates on frictionless air bearings about its vertical axis at 7.73 rpm. An 88.5-kg man standing at the very center of the platform starts walking (at t = 0) radially outward at a speed of 0.531 m/s with respect to the platform. Approximating the man by a vertical cylinder of radius Rm = 0.205 m, determine an equation (specific expression) for the angular velocity of the platform as a function of time. What is the angular velocity when the man reaches the edge of the platform?

Explanation / Answer

we should apply conservation of angular momentum ;

( I1 + I2 ) = ( I1 + I2 ) ;

( 0.5 * 327 * 4.51^2 + 0 ) ( 7.73 ) = ( 0.5 * 327 * 4.51^2 + 0.5 * 88.5 * 0.205^2 + 88.5 * r^2 ) ;

25706.9 = ( 3327.46 + 88.5 r^2 ) ;

r = 0.531 t ;

25706.9 = ( 3327.46 + 88.5 ( 0.531 t ) ^2 ) ;

25706.9 = ( 3327.46 + 24.953 t^2 ) ;

= 25706.9 / [ 3327.46 + 24.953 t^2 ] <----------in RPM ,<-----ans

= 2692.020 / [ 3327.46 + 24.953 t^2 ] <-------in rad / s <----

wen the man reaches paltform

25706.9 = ( 3327.46 + 88.5 * 4.51 ^2 ) ;

= 5.0134 rpm <----------ans wen he raches the edge

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