ANGULAR MOMENTUM \& CONSERVATION OF ANGULAR MOMENTUM
Rotational Motion

269405 A ballet dancer is rotating about his own vertical axis at an angular velocity\(100 \mathrm{rpm}\) on smooth horizontal floor. The ballet dancer folds himself close to his axis of rotation by which is moment of inertia decreases to half of initial moment of inertia then his final angular velocity is

1 \(50 \mathrm{rpm}\)
2 \(100 \mathrm{rpm}\)
3 \(150 \mathrm{rpm}\)
4 \(200 \mathrm{rpm}\)
Rotational Motion

269406 A circular ring of mass\(M\) is rotating about its own axis in horizontal plane at an angular velocity \(\omega\). If two point size bodies each of mass \(m\), are gently attached to the rim of ring at two ends of its diameter, then the angular velocity of ring is

1 \(\frac{M \omega}{M+2 m}\)
2 \(\frac{2 m \omega}{M+2 m}\)
3 \(\frac{m \omega}{M+2 m}\)
4 \(\frac{2 M \omega}{M+2 m}\)
Rotational Motion

269407 A ballet dancer is rotating at angular velocity\(\omega\) on smooth horizontal floor. The ballet dancer folds his body close to his axis of rotation by which his radius of gyration decreases by \(1 / 4^{\text {th }}\) of his initial radius of gyration, his final angular velocity is

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

269408 A particle of mass\(m\) is moving along a circle of radius \(r\) with a time period T. Its angular momentum is

1 \(\frac{2 \pi m r}{T}\)
2 \(\frac{4 \pi m r}{T}\)
3 \(\frac{2 \pi m r^{2}}{T}\)
4 \(\frac{4 \pi m r^{2}}{T}\)
Rotational Motion

269405 A ballet dancer is rotating about his own vertical axis at an angular velocity\(100 \mathrm{rpm}\) on smooth horizontal floor. The ballet dancer folds himself close to his axis of rotation by which is moment of inertia decreases to half of initial moment of inertia then his final angular velocity is

1 \(50 \mathrm{rpm}\)
2 \(100 \mathrm{rpm}\)
3 \(150 \mathrm{rpm}\)
4 \(200 \mathrm{rpm}\)
Rotational Motion

269406 A circular ring of mass\(M\) is rotating about its own axis in horizontal plane at an angular velocity \(\omega\). If two point size bodies each of mass \(m\), are gently attached to the rim of ring at two ends of its diameter, then the angular velocity of ring is

1 \(\frac{M \omega}{M+2 m}\)
2 \(\frac{2 m \omega}{M+2 m}\)
3 \(\frac{m \omega}{M+2 m}\)
4 \(\frac{2 M \omega}{M+2 m}\)
Rotational Motion

269407 A ballet dancer is rotating at angular velocity\(\omega\) on smooth horizontal floor. The ballet dancer folds his body close to his axis of rotation by which his radius of gyration decreases by \(1 / 4^{\text {th }}\) of his initial radius of gyration, his final angular velocity is

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

269408 A particle of mass\(m\) is moving along a circle of radius \(r\) with a time period T. Its angular momentum is

1 \(\frac{2 \pi m r}{T}\)
2 \(\frac{4 \pi m r}{T}\)
3 \(\frac{2 \pi m r^{2}}{T}\)
4 \(\frac{4 \pi m r^{2}}{T}\)
Rotational Motion

269405 A ballet dancer is rotating about his own vertical axis at an angular velocity\(100 \mathrm{rpm}\) on smooth horizontal floor. The ballet dancer folds himself close to his axis of rotation by which is moment of inertia decreases to half of initial moment of inertia then his final angular velocity is

1 \(50 \mathrm{rpm}\)
2 \(100 \mathrm{rpm}\)
3 \(150 \mathrm{rpm}\)
4 \(200 \mathrm{rpm}\)
Rotational Motion

269406 A circular ring of mass\(M\) is rotating about its own axis in horizontal plane at an angular velocity \(\omega\). If two point size bodies each of mass \(m\), are gently attached to the rim of ring at two ends of its diameter, then the angular velocity of ring is

1 \(\frac{M \omega}{M+2 m}\)
2 \(\frac{2 m \omega}{M+2 m}\)
3 \(\frac{m \omega}{M+2 m}\)
4 \(\frac{2 M \omega}{M+2 m}\)
Rotational Motion

269407 A ballet dancer is rotating at angular velocity\(\omega\) on smooth horizontal floor. The ballet dancer folds his body close to his axis of rotation by which his radius of gyration decreases by \(1 / 4^{\text {th }}\) of his initial radius of gyration, his final angular velocity is

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

269408 A particle of mass\(m\) is moving along a circle of radius \(r\) with a time period T. Its angular momentum is

1 \(\frac{2 \pi m r}{T}\)
2 \(\frac{4 \pi m r}{T}\)
3 \(\frac{2 \pi m r^{2}}{T}\)
4 \(\frac{4 \pi m r^{2}}{T}\)
Rotational Motion

269405 A ballet dancer is rotating about his own vertical axis at an angular velocity\(100 \mathrm{rpm}\) on smooth horizontal floor. The ballet dancer folds himself close to his axis of rotation by which is moment of inertia decreases to half of initial moment of inertia then his final angular velocity is

1 \(50 \mathrm{rpm}\)
2 \(100 \mathrm{rpm}\)
3 \(150 \mathrm{rpm}\)
4 \(200 \mathrm{rpm}\)
Rotational Motion

269406 A circular ring of mass\(M\) is rotating about its own axis in horizontal plane at an angular velocity \(\omega\). If two point size bodies each of mass \(m\), are gently attached to the rim of ring at two ends of its diameter, then the angular velocity of ring is

1 \(\frac{M \omega}{M+2 m}\)
2 \(\frac{2 m \omega}{M+2 m}\)
3 \(\frac{m \omega}{M+2 m}\)
4 \(\frac{2 M \omega}{M+2 m}\)
Rotational Motion

269407 A ballet dancer is rotating at angular velocity\(\omega\) on smooth horizontal floor. The ballet dancer folds his body close to his axis of rotation by which his radius of gyration decreases by \(1 / 4^{\text {th }}\) of his initial radius of gyration, his final angular velocity is

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

269408 A particle of mass\(m\) is moving along a circle of radius \(r\) with a time period T. Its angular momentum is

1 \(\frac{2 \pi m r}{T}\)
2 \(\frac{4 \pi m r}{T}\)
3 \(\frac{2 \pi m r^{2}}{T}\)
4 \(\frac{4 \pi m r^{2}}{T}\)