SATHEE: Rotational Motion Question 54

Rotational Motion Question 54

Question: A round disc of moment of inertia $I_{2}$ about its axis perpendicular to its plane and passing through its centre is placed over another disc of moment of inertia $I_{1}$ 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) $\frac{I_{2} ω}{I_{1} + I_{2}}$

B) $ω$

C) $\frac{I_{1} ω}{I_{1} + I_{2}}$

D) $\frac{(I_{1} + I_{2}) ω}{I_{1}}$

Show Answer

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 $I_{1}$ and rotating about its axis with angular velocity $ω$ is

$L_{1} = I_{1} ω$

When a round disc of moment of inertia $I_{2}$ is placed on first disc, then angular momentum of the combination is

$L_{2} = (I_{1} + I_{2}) ω$

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

$L_{1} = L_{2}$

$I_{1} ω = (I_{1} + I_{2}) ω$

$\Rightarrow$ $ω ‘ = \frac{I_{2} ω}{I + I_{2}}$

Rotational Motion Question 54

Question: A round disc of moment of inertia $I_{2}$ about its axis perpendicular to its plane and passing through its centre is placed over another disc of moment of inertia $I_{1}$ rotating with an angular velocity $ω$ about the same axis. The final angular velocity of the combination of discs is:

Options:

Answer:

Solution:

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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:

Options:

Answer:

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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