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A man weighing 60kg stands on an immobile platform ( a disc) with a mass of 100 kg.What are the no. of revolutions per minute made by the platform if the man moves along a circle with a radius of 5 mts. around the axis of rotation? Given that the man moves relative to the platform with a velocity of 4 km/h.The radius of platform is 10 mts.
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2 Answers
262since total torque about center of disc =0 ,
angular momentum remains constant.
thus ,
Li =Lf
or , 0 = Lman + Ldisc
Lman = - Ldisc
now Lman =mvr = 60*v1*5
Ldisc = -Iω = -12MR2.ω = 12*100*10*10*ω
thus equating the two ,
300v1 = 5000ω
or , 3v1 = 50ω
now velocity of disc at 5 mts =v2= 5ω
or , 3v1 =10v2 ...(i)
now relative velocity = 4*518m/s = 109 m/s = v1 +v2 ....(ii)
from i) and ii) v2 = 1013m/s
thus ω = 213 rad/s
thus number of rev. in a min = 60 * ω2π = 6013π