1could u provide a rough sketch
A semicircular thin coil of mass M kg and radius R m is hindged at one end A and lies in a vertical plane. At time t=0 the coil was ignited to burn its mass at constant rate K kg/s. Assuming total conversion of mass into energy, find angular velocity of the coil about A at any time t . Contacts are frictionless.
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2 Answers
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E=mc2
Now E=(1/2)Ipω2
dE/dt=d(mc2)/dt
dE/dt=c2dm/dt ..(c=a 'big' constant :P)
dE/dt=c2K
d((1/2)Ipω2)/dt=Kc2
Ipωdω/dt=Kc2
ωdω/dt=Kc2/Ip
integrating it with ω=0 at t=0 to ω=w at t=t
ω2/2=Kc2t/Ip
ω=√2Kc2t/Ip
where Ip=2MR2