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A round disc of moment of inertia I₂ about its axis perpendicular to its plane and passing through its centre is placed over another disc of moment of inertia I₁ rotating with an angular velocity ω about the same axis. The final angular velocity of the combination of discs is

Asked in CBSE AIPMT 2004 · Conservation of angular momentum

• (1) (I₂ω)/(I₁+I₂)
• (2) ω
• (3) (I₁ω)/(I₁+I₂)
• (4) ((I₁+I₂)ω)/(I₁)

Step-by-step solution

Why the other options are wrong

• (1) comes from puts the wrong disc in the numerator: the angular momentum brought into the collision is I₁ω, carried by the disc that was already spinning
• (2) comes from assuming the added disc changes nothing; the combined moment of inertia is larger, so the shared angular velocity must be smaller
• (4) comes from the ratio inverted, which would have the system speed up when mass is added to it

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