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Question

# Two discs are rotating about their axes, normal to the plane of the discs and passing through the centre of the discs. Disc D has 2 kg mass and 0.2 m radius and initial angular velocity of 50 rad/s. Disc D2 has 4 kg mass, 0.1 m radius and initial angular velocity of 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

A
50 rad/s
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B
20 rad/s
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C
100 rad/s
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D
200 rad/s
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Solution

## The correct option is C 100 rad/sMOI of disc D, about an axis passing through its centre and normal to its plane. I1=MR22=2×(0.2)22=0.04 kg-m2 Initial angular velocity of disc D1, ω1=50 rad/s MOI of disc D2 about an axis passing through its centre and normal to the plane. I2=MR22=4×(0.1)22 =0.02 kg-m2 Initial angular velocity of disc D2, ω2=200 rad/s Total angular momentum of the two discs, initially is Li=I1ω1+I2ω2 When both discs are brought in contact, axes of rotation coincide. Consider both discs as a system. Hence, final angular momentum of the system is, Lf=(I1+I2)ω Here, ω is the final angular speed of the system. According to the law of conservation of angular momentum, we get, Li=Lf I1ω1+I2ω2=(I1+I2)ω ⇒ω=(0.04)×(50)+(0.02)×(200)(0.04+0.02) ⇒ω=100 rad/s

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