CIRCULAR MOTION

since total torque about center of disc =0 ,
angular momentum remains constant.
thus ,

L_i =L_f
or , 0 = L_man + L_disc

L_man = - L_disc

now L_man =mvr = 60*v₁*5
L_disc = -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