Rotational Motion Question 54

Question: 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:

[AIPMT (S) 2004]

Options:

A) I2ωI1+I2

B) ω

C) I1ωI1+I2

D) (I1+I2)ωI1

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Answer:

Correct Answer: A

Solution:

  • Key Idea: When no external torque acts on a system of particles, then the total angular momentum of the system remains always a constant.

The angular momentum of a disc of moment of inertia I1 and rotating about its axis with angular velocity ω is

L1=I1ω

When a round disc of moment of inertia I2 is placed on first disc, then angular momentum of the combination is

L2=(I1+I2)ω

In the absence of any external torque, angular momentum remains conserved i.e.,

L1=L2

I1ω=(I1+I2)ω

ω=I2ωI+I2



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