physics_doubth_questions Physics doubt questions
Q-1. A flywheel in form of disc is rotating about an axis passing thru the center and perpendicular to the plane looses 100J of energy when slowing down from 60 rpm to 30 rpm. Find the moment of inertia about the same axis and change in angular momentum. Answer-1:𝜔1=60rpm=2𝜋rad/sec𝜔2=30rpm=𝜋rad/secLoss in energy = 100 J Initial kinetic energy =K1=12I𝜔12=12I(2𝜋)2 Final kinetic energy =K2=12I𝜔22=12I(𝜋)2 Loss in kinetic energy =K1-K2=12I[(2𝜋)2-(𝜋)2] 12I[(2𝜋)2-(𝜋)2]=100⟹I=2003𝜋2=6.754kgm2Change in momentum=I(𝜔1-𝜔2)=2003𝜋2×(2𝜋-𝜋)=21.22kgm2/sec
Q-2. Two wheels of moment of inertia 4kgm2 rorate side by side at the rate of 120 rev/min and 240 rev/min respectively. in opposite directions. If now both the wheels are coupled by means of weightless shaft so that bothe the wheels now rotate with common angular speed. Find the new speed of rotation. Answer-2:𝜔1=120rpm=4𝜋rad/sec𝜔2=240rpm=8𝜋rad/sec in opposite directionLetcommonangularspeed=𝜔 Total Initial momentum=L=4×8𝜋-4×4𝜋=16𝜋kgm2/sec When wheels are joined the moment of inertia = 4 + 4=8kgm2 8𝜔=16𝜋⟹𝜔=2𝜋rad/sec=60rpm