ANGULAR MOMENTUM \& CONSERVATION OF ANGULAR MOMENTUM
Rotational Motion

269531 A uniform cylindrical rod of mass\(m\) and length \(L\) is rotating with an angular velocity \(\omega\). The axis of rotation is perpendicular to its axis of symmetry and passes through one of its edge faces. If the room temperature increases by ' \(t\) ' and the coefficient of linear expansion is \(\alpha\), the change in its angular velocity is

1 \(2 \alpha \omega t\)
2 \(\alpha \omega t\)
3 \(\frac{3}{2} \alpha \omega t\)
4 \(\frac{\alpha \omega t}{2}\)
Rotational Motion

269579 A circular disc is rotating without friction about its natural axis with an angular velocity \(\omega\). Another circular disc of same material and thickness but half the radius is gently placed over it coaxially. The angular velocity of composite disc will be

1 \(\frac{4 \omega}{3}\)
2 \(\frac{8 \omega}{9}\)
3 \(\frac{7 \omega}{8}\)
4 \(\frac{16 \omega}{17}\)
Rotational Motion

269580 A ballet dancer is rotating about his own vertical axis on smooth horizontal floor with a time period \(0.5 \mathrm{sec}\). The dancer folds himself close to his axis of rotation due to which his radius of gyration decreases by \(20 \%\), then his time period is

1 \(0.1 \mathrm{sec}\)
2 \(0.25 \mathrm{sec}\)
3 \(0.32 \mathrm{sec}\)
4 \(0.4 \mathrm{sec}\)
Rotational Motion

269581 A particle of mass \(1 \mathrm{~kg}\) is moving along the line \(y=x+2\) with speed \(2 \mathrm{~m} / \mathrm{sec}\). The magnitude of angular momentum of the particle about the origin is

1 \(4 \mathrm{~kg}-\mathrm{m}^{2} / \mathrm{sec}\)
2 \(2 \sqrt{2} \mathrm{~kg}-\mathrm{m}^{2} / \mathrm{sec}\)
3 \(4 \sqrt{2} \mathrm{~kg}-\mathrm{m}^{2} / \mathrm{sec}\)
4 \(2 \mathrm{~kg}-\mathrm{m}^{2} / \mathrm{sec}\)
Rotational Motion

269582 A uniform metal rod of length \(L\) and mass \(M\) is rotating about an axis passing through one of the ends perpendicular to the rod with angular speed \(\omega\). If the temperature increases by \(t^{\circ} \mathrm{C}\) then the change in its angular velocity is proportional to which of the following?(Coefficient of linear expansion of \(\operatorname{rod}=\alpha)\).

1 \(\sqrt{\omega}\)
2 \(\omega\)
3 \(\omega^{2}\)
4 \(\frac{1}{\omega}\)
Rotational Motion

269531 A uniform cylindrical rod of mass\(m\) and length \(L\) is rotating with an angular velocity \(\omega\). The axis of rotation is perpendicular to its axis of symmetry and passes through one of its edge faces. If the room temperature increases by ' \(t\) ' and the coefficient of linear expansion is \(\alpha\), the change in its angular velocity is

1 \(2 \alpha \omega t\)
2 \(\alpha \omega t\)
3 \(\frac{3}{2} \alpha \omega t\)
4 \(\frac{\alpha \omega t}{2}\)
Rotational Motion

269579 A circular disc is rotating without friction about its natural axis with an angular velocity \(\omega\). Another circular disc of same material and thickness but half the radius is gently placed over it coaxially. The angular velocity of composite disc will be

1 \(\frac{4 \omega}{3}\)
2 \(\frac{8 \omega}{9}\)
3 \(\frac{7 \omega}{8}\)
4 \(\frac{16 \omega}{17}\)
Rotational Motion

269580 A ballet dancer is rotating about his own vertical axis on smooth horizontal floor with a time period \(0.5 \mathrm{sec}\). The dancer folds himself close to his axis of rotation due to which his radius of gyration decreases by \(20 \%\), then his time period is

1 \(0.1 \mathrm{sec}\)
2 \(0.25 \mathrm{sec}\)
3 \(0.32 \mathrm{sec}\)
4 \(0.4 \mathrm{sec}\)
Rotational Motion

269581 A particle of mass \(1 \mathrm{~kg}\) is moving along the line \(y=x+2\) with speed \(2 \mathrm{~m} / \mathrm{sec}\). The magnitude of angular momentum of the particle about the origin is

1 \(4 \mathrm{~kg}-\mathrm{m}^{2} / \mathrm{sec}\)
2 \(2 \sqrt{2} \mathrm{~kg}-\mathrm{m}^{2} / \mathrm{sec}\)
3 \(4 \sqrt{2} \mathrm{~kg}-\mathrm{m}^{2} / \mathrm{sec}\)
4 \(2 \mathrm{~kg}-\mathrm{m}^{2} / \mathrm{sec}\)
Rotational Motion

269582 A uniform metal rod of length \(L\) and mass \(M\) is rotating about an axis passing through one of the ends perpendicular to the rod with angular speed \(\omega\). If the temperature increases by \(t^{\circ} \mathrm{C}\) then the change in its angular velocity is proportional to which of the following?(Coefficient of linear expansion of \(\operatorname{rod}=\alpha)\).

1 \(\sqrt{\omega}\)
2 \(\omega\)
3 \(\omega^{2}\)
4 \(\frac{1}{\omega}\)
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Rotational Motion

269531 A uniform cylindrical rod of mass\(m\) and length \(L\) is rotating with an angular velocity \(\omega\). The axis of rotation is perpendicular to its axis of symmetry and passes through one of its edge faces. If the room temperature increases by ' \(t\) ' and the coefficient of linear expansion is \(\alpha\), the change in its angular velocity is

1 \(2 \alpha \omega t\)
2 \(\alpha \omega t\)
3 \(\frac{3}{2} \alpha \omega t\)
4 \(\frac{\alpha \omega t}{2}\)
Rotational Motion

269579 A circular disc is rotating without friction about its natural axis with an angular velocity \(\omega\). Another circular disc of same material and thickness but half the radius is gently placed over it coaxially. The angular velocity of composite disc will be

1 \(\frac{4 \omega}{3}\)
2 \(\frac{8 \omega}{9}\)
3 \(\frac{7 \omega}{8}\)
4 \(\frac{16 \omega}{17}\)
Rotational Motion

269580 A ballet dancer is rotating about his own vertical axis on smooth horizontal floor with a time period \(0.5 \mathrm{sec}\). The dancer folds himself close to his axis of rotation due to which his radius of gyration decreases by \(20 \%\), then his time period is

1 \(0.1 \mathrm{sec}\)
2 \(0.25 \mathrm{sec}\)
3 \(0.32 \mathrm{sec}\)
4 \(0.4 \mathrm{sec}\)
Rotational Motion

269581 A particle of mass \(1 \mathrm{~kg}\) is moving along the line \(y=x+2\) with speed \(2 \mathrm{~m} / \mathrm{sec}\). The magnitude of angular momentum of the particle about the origin is

1 \(4 \mathrm{~kg}-\mathrm{m}^{2} / \mathrm{sec}\)
2 \(2 \sqrt{2} \mathrm{~kg}-\mathrm{m}^{2} / \mathrm{sec}\)
3 \(4 \sqrt{2} \mathrm{~kg}-\mathrm{m}^{2} / \mathrm{sec}\)
4 \(2 \mathrm{~kg}-\mathrm{m}^{2} / \mathrm{sec}\)
Rotational Motion

269582 A uniform metal rod of length \(L\) and mass \(M\) is rotating about an axis passing through one of the ends perpendicular to the rod with angular speed \(\omega\). If the temperature increases by \(t^{\circ} \mathrm{C}\) then the change in its angular velocity is proportional to which of the following?(Coefficient of linear expansion of \(\operatorname{rod}=\alpha)\).

1 \(\sqrt{\omega}\)
2 \(\omega\)
3 \(\omega^{2}\)
4 \(\frac{1}{\omega}\)
Rotational Motion

269531 A uniform cylindrical rod of mass\(m\) and length \(L\) is rotating with an angular velocity \(\omega\). The axis of rotation is perpendicular to its axis of symmetry and passes through one of its edge faces. If the room temperature increases by ' \(t\) ' and the coefficient of linear expansion is \(\alpha\), the change in its angular velocity is

1 \(2 \alpha \omega t\)
2 \(\alpha \omega t\)
3 \(\frac{3}{2} \alpha \omega t\)
4 \(\frac{\alpha \omega t}{2}\)
Rotational Motion

269579 A circular disc is rotating without friction about its natural axis with an angular velocity \(\omega\). Another circular disc of same material and thickness but half the radius is gently placed over it coaxially. The angular velocity of composite disc will be

1 \(\frac{4 \omega}{3}\)
2 \(\frac{8 \omega}{9}\)
3 \(\frac{7 \omega}{8}\)
4 \(\frac{16 \omega}{17}\)
Rotational Motion

269580 A ballet dancer is rotating about his own vertical axis on smooth horizontal floor with a time period \(0.5 \mathrm{sec}\). The dancer folds himself close to his axis of rotation due to which his radius of gyration decreases by \(20 \%\), then his time period is

1 \(0.1 \mathrm{sec}\)
2 \(0.25 \mathrm{sec}\)
3 \(0.32 \mathrm{sec}\)
4 \(0.4 \mathrm{sec}\)
Rotational Motion

269581 A particle of mass \(1 \mathrm{~kg}\) is moving along the line \(y=x+2\) with speed \(2 \mathrm{~m} / \mathrm{sec}\). The magnitude of angular momentum of the particle about the origin is

1 \(4 \mathrm{~kg}-\mathrm{m}^{2} / \mathrm{sec}\)
2 \(2 \sqrt{2} \mathrm{~kg}-\mathrm{m}^{2} / \mathrm{sec}\)
3 \(4 \sqrt{2} \mathrm{~kg}-\mathrm{m}^{2} / \mathrm{sec}\)
4 \(2 \mathrm{~kg}-\mathrm{m}^{2} / \mathrm{sec}\)
Rotational Motion

269582 A uniform metal rod of length \(L\) and mass \(M\) is rotating about an axis passing through one of the ends perpendicular to the rod with angular speed \(\omega\). If the temperature increases by \(t^{\circ} \mathrm{C}\) then the change in its angular velocity is proportional to which of the following?(Coefficient of linear expansion of \(\operatorname{rod}=\alpha)\).

1 \(\sqrt{\omega}\)
2 \(\omega\)
3 \(\omega^{2}\)
4 \(\frac{1}{\omega}\)
Rotational Motion

269531 A uniform cylindrical rod of mass\(m\) and length \(L\) is rotating with an angular velocity \(\omega\). The axis of rotation is perpendicular to its axis of symmetry and passes through one of its edge faces. If the room temperature increases by ' \(t\) ' and the coefficient of linear expansion is \(\alpha\), the change in its angular velocity is

1 \(2 \alpha \omega t\)
2 \(\alpha \omega t\)
3 \(\frac{3}{2} \alpha \omega t\)
4 \(\frac{\alpha \omega t}{2}\)
Rotational Motion

269579 A circular disc is rotating without friction about its natural axis with an angular velocity \(\omega\). Another circular disc of same material and thickness but half the radius is gently placed over it coaxially. The angular velocity of composite disc will be

1 \(\frac{4 \omega}{3}\)
2 \(\frac{8 \omega}{9}\)
3 \(\frac{7 \omega}{8}\)
4 \(\frac{16 \omega}{17}\)
Rotational Motion

269580 A ballet dancer is rotating about his own vertical axis on smooth horizontal floor with a time period \(0.5 \mathrm{sec}\). The dancer folds himself close to his axis of rotation due to which his radius of gyration decreases by \(20 \%\), then his time period is

1 \(0.1 \mathrm{sec}\)
2 \(0.25 \mathrm{sec}\)
3 \(0.32 \mathrm{sec}\)
4 \(0.4 \mathrm{sec}\)
Rotational Motion

269581 A particle of mass \(1 \mathrm{~kg}\) is moving along the line \(y=x+2\) with speed \(2 \mathrm{~m} / \mathrm{sec}\). The magnitude of angular momentum of the particle about the origin is

1 \(4 \mathrm{~kg}-\mathrm{m}^{2} / \mathrm{sec}\)
2 \(2 \sqrt{2} \mathrm{~kg}-\mathrm{m}^{2} / \mathrm{sec}\)
3 \(4 \sqrt{2} \mathrm{~kg}-\mathrm{m}^{2} / \mathrm{sec}\)
4 \(2 \mathrm{~kg}-\mathrm{m}^{2} / \mathrm{sec}\)
Rotational Motion

269582 A uniform metal rod of length \(L\) and mass \(M\) is rotating about an axis passing through one of the ends perpendicular to the rod with angular speed \(\omega\). If the temperature increases by \(t^{\circ} \mathrm{C}\) then the change in its angular velocity is proportional to which of the following?(Coefficient of linear expansion of \(\operatorname{rod}=\alpha)\).

1 \(\sqrt{\omega}\)
2 \(\omega\)
3 \(\omega^{2}\)
4 \(\frac{1}{\omega}\)