The discs are rotating about their axes, normal to the discs and passing through the centres of the discs. Disc D1 has 2kg mass and 0.2m radius and initial angular velocity of 50 rad/s. Disc D2 has 4kg mass, 0.1m 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 angular velocity of the system is

I1=MR22=2×(0.2)22=0.04kgm2,ω1=50rad/sI2=4×(0.1)22=0.02kgm2,w2=200rad/sω=I1ω1+I2ω2I1+I2=0.04×50+0.02×2000.04+0.02ω=60.06=100rad/s

The discs are rotating about their axes, normal to the discs and passing through the centres of the discs. Disc D1 has 2kg mass and 0.2m radius and initial angular velocity of 50 rad/s. Disc D2 has 4kg mass, 0.1m 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 angular velocity of the system is

I1=MR22=2×(0.2)22=0.04kgm2,ω1=50rad/sI2=4×(0.1)22=0.02kgm2,w2=200rad/sω=I1ω1+I2ω2I1+I2=0.04×50+0.02×2000.04+0.02ω=60.06=100rad/s

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The discs are rotating about their axes, normal to the discs and passing through the centres of the discs. Disc D₁ has 2kg mass and 0.2m radius and initial angular velocity of 50 rad/s. Disc D₂ has 4kg mass, 0.1m 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 angular velocity of the system is

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Detailed Solution

$I_{1} = \frac{{MR}^{2}}{2} = \frac{2 \times (0 .2)^{2}}{2} = 0 .04 {kgm}^{2}$ , $ω_{1} = 50 rad / s$

$I_{2} = \frac{4 \times (0 .1)^{2}}{2} = 0 .02 {kgm}^{2}$ , $w_{2} = 200 rad / s$

$ω = \frac{I_{1} ω_{1} + I_{2} ω_{2}}{I_{1} + I_{2}} = \frac{0.04 \times 50 + 0.02 \times 200}{0.04 + 0.02}$

$ω = \frac{6}{0.06} = 100 rad / s$

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