A nitrogen molecule has two nitrogen atoms separated by a distance of 1 . 3 × 10 - 10 m . Find its moment of inertia about the centre of mass. If its rotational kinetic energy is 4 × 10 - 21 J . Then compute its frequency of rotation about the centre of mass. The mass of a nitrogen atom is 14 amu ( 1 amu = 1 . 66 × 10 - 27 kg )

Mass of the nitrogen atom 14 × 1 . 66 × 10 - 27 = 23 . 24 × 10 - 27 kg The moment of inertia of Nitrogen molecule= I = mass of tye N 2 molecule × ( distance from the axis ) 2 Since the molecule has two atoms and the distance from the axis is half of the interatomic distance, so the moment of inertia of the molecule is I = 1 2 m r 2 2 + 1 2 m r 2 2 = 2 × 23 . 24 × 10 - 27 × 1 . 3 × 10 - 10 2 2 = 19 . 63 × 10 - 47 kgm 2 Now the kinetic energy of the rotation is given by Where ω = angular velocity K = 1 2 Iω 2 = 1 2 × 19 . 63 × 10 - 47 ω 2 so that ω = 0 . 638 × 10 13 rads - 1 Since ω = 2 πf or f = ω 2 π = 0 . 638 × 10 13 2 × 3 . 16 = 10 2 Hz

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Define angular momentum. Derive relation between angular momentum and moment of inertia, of a rigid body.

Important Questions on Rotational Motion of a Rigid Body : Moment of Inertia

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11th ICSE

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ISC Physics Class XI Part 1>Chapter 14 - Rotational Motion of a Rigid Body : Moment of Inertia>QUESTIONS>Q 10

Derive a relation between torque and angular momentum and establish from it the principle of conservation of angular momentum.

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ISC Physics Class XI Part 1>Chapter 14 - Rotational Motion of a Rigid Body : Moment of Inertia>QUESTIONS>Q 11

Explain the law of conservation of angular momentum with an example.

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ISC Physics Class XI Part 1>Chapter 14 - Rotational Motion of a Rigid Body : Moment of Inertia>QUESTIONS>Q 14

Derive an expression for the moment of inertia of a uniform disc about its diameter.

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ISC Physics Class XI Part 1>Chapter 14 - Rotational Motion of a Rigid Body : Moment of Inertia>QUESTIONS>Q 15

Compare among the parameters of translatory motion with corresponding parameters of rotational motion Explain how the centre of mass of a rotating rigid body is representative of translatory motion?

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ISC Physics Class XI Part 1>Chapter 14 - Rotational Motion of a Rigid Body : Moment of Inertia>NUMERICALS>Q 1

A body of mass

50 g

is revolving around an axis around a circular path. The distance of the centre of the mass of the body from the axis of rotation is

50 cm

. Find the moment of inertia of the body.

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ISC Physics Class XI Part 1>Chapter 14 - Rotational Motion of a Rigid Body : Moment of Inertia>NUMERICALS>Q 2

Find the moment of inertia of the hydrogen molecule about an axis passing through its centre of mass and perpendicular to the inter nuclear axis (mass of the hydrogen atom = $1.7 \times 10^{- 27} kg$ Inter atomic distance = $4 \times 10^{- 10} m$

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11th ICSE

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ISC Physics Class XI Part 1>Chapter 14 - Rotational Motion of a Rigid Body : Moment of Inertia>NUMERICALS>Q 3

A nitrogen molecule has two nitrogen atoms separated by a distance of $1.3 \times 10^{- 10} m$ . Find its moment of inertia about the centre of mass. If its rotational kinetic energy is $4 \times 10^{- 21} J$ . Then compute its frequency of rotation about the centre of mass. The mass of a nitrogen atom is $14 amu$ ( $1 amu = 1.66 \times 10^{- 27} kg$ )

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11th ICSE

IMPORTANT

ISC Physics Class XI Part 1>Chapter 14 - Rotational Motion of a Rigid Body : Moment of Inertia>NUMERICALS>Q 4

Three particles (each of mass $10 g$ ) are situated at the three corners of an equilateral triangle of side $5 cm$ . Determine the moment of inertia of this system about an axis passing through one corner of the triangle and perpendicular to the plane of the triangle.

Define angular momentum. Derive relation between angular momentum and moment of inertia, of a rigid body.

Important Questions on Rotational Motion of a Rigid Body : Moment of Inertia

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