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Question

Two discs are rotating about their axes, normal to the disc and passing through the centres of the discs. Disc D1 has 2 kg mass and 0.2 m radius and its initial angular velocity is 50 rad/s. Disc D2 has 4 kg mass, 0.1 m radius and its initial angular velocity is 200 rad/s. The two discs are brought in contact face to face, with their axes of rotation coincident. The final angular velocity (in rad/s) of the system is

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Solution

Given for disc D1 :
Mass of disc m1=2 kg
ω1=50 rad/s
r1=0.2 m
I1=m1r212=2×(0.2)22
=0.04 kg m2/s

For disc D2 :
Mass of disc m2=4 kg
ω2=200 rad/s
r2=0.1 m
I2=m2r222=4×(0.1)22
=0.02 kg m2/s

If we take disc D1 and D2 as a system, torque between D1 & D2 will be internal, so there will be no external torque. Hence, angular momentum is conserved.
Li=Lf
I1ω1+I2ω2=(I1+I2)ω
(0.04)×50+(0.02)×200=(0.04+0.02)ω
ω=100 rad/s

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