Angular Momentum and its Conservation for a Rigid Body
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365633 A particle performs uniform circular motion with an angular momentum \(L\). If the frequency of particle motion is doubled and its kinetic energy is halved, the angular momentum becomes

1 \(2 L\)
2 \(4 L\)
3 \(\dfrac{L}{2}\)
4 \(\dfrac{L}{4}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365634 A spherical body of mass \({m}\) and radius \({r}\) is released from rest along a smooth inclined plane of inclination \({\theta}\). The angular momentum of the body about the instantaneous point of contact after a time ' \({t}\) ' from the instant of release is

1 \({m g r t \cos \theta}\)
2 \({m g r t \sin \theta}\)
3 \({\dfrac{3}{2} m g r t \sin \theta}\)
4 None of these
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365635 A rod of mass \(m\) and length \(l\) is moving with linear velocity \(v\) and angular velocity \(\omega\). The angular momentum of the rod about point \(P\) is
supporting img

1 \(\dfrac{m v l}{2}\)
2 \(\dfrac{m v l}{2}+\dfrac{m l^{2}}{12} \omega\)
3 \(\dfrac{m l^{2} \omega}{12}\)
4 \(m v l\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365636 A sphere of mass \(M\) rolls without slipping on a rough surface with centre of mass has constant speed \(v_{0}\). If mass of the sphere is \(m\) and its radius be \(R\), then the angular momentum of the sphere about the point of contact is

1 \(-M v R(\hat{k})\)
2 \(\dfrac{5}{4} M v_{0} R(-\hat{k})\)
3 \(\dfrac{7}{5} M v_{0} R(-\hat{k})\)
4 \(\dfrac{9}{5} M v_{0} R(-\hat{k})\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365633 A particle performs uniform circular motion with an angular momentum \(L\). If the frequency of particle motion is doubled and its kinetic energy is halved, the angular momentum becomes

1 \(2 L\)
2 \(4 L\)
3 \(\dfrac{L}{2}\)
4 \(\dfrac{L}{4}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365634 A spherical body of mass \({m}\) and radius \({r}\) is released from rest along a smooth inclined plane of inclination \({\theta}\). The angular momentum of the body about the instantaneous point of contact after a time ' \({t}\) ' from the instant of release is

1 \({m g r t \cos \theta}\)
2 \({m g r t \sin \theta}\)
3 \({\dfrac{3}{2} m g r t \sin \theta}\)
4 None of these
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365635 A rod of mass \(m\) and length \(l\) is moving with linear velocity \(v\) and angular velocity \(\omega\). The angular momentum of the rod about point \(P\) is
supporting img

1 \(\dfrac{m v l}{2}\)
2 \(\dfrac{m v l}{2}+\dfrac{m l^{2}}{12} \omega\)
3 \(\dfrac{m l^{2} \omega}{12}\)
4 \(m v l\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365636 A sphere of mass \(M\) rolls without slipping on a rough surface with centre of mass has constant speed \(v_{0}\). If mass of the sphere is \(m\) and its radius be \(R\), then the angular momentum of the sphere about the point of contact is

1 \(-M v R(\hat{k})\)
2 \(\dfrac{5}{4} M v_{0} R(-\hat{k})\)
3 \(\dfrac{7}{5} M v_{0} R(-\hat{k})\)
4 \(\dfrac{9}{5} M v_{0} R(-\hat{k})\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365633 A particle performs uniform circular motion with an angular momentum \(L\). If the frequency of particle motion is doubled and its kinetic energy is halved, the angular momentum becomes

1 \(2 L\)
2 \(4 L\)
3 \(\dfrac{L}{2}\)
4 \(\dfrac{L}{4}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365634 A spherical body of mass \({m}\) and radius \({r}\) is released from rest along a smooth inclined plane of inclination \({\theta}\). The angular momentum of the body about the instantaneous point of contact after a time ' \({t}\) ' from the instant of release is

1 \({m g r t \cos \theta}\)
2 \({m g r t \sin \theta}\)
3 \({\dfrac{3}{2} m g r t \sin \theta}\)
4 None of these
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365635 A rod of mass \(m\) and length \(l\) is moving with linear velocity \(v\) and angular velocity \(\omega\). The angular momentum of the rod about point \(P\) is
supporting img

1 \(\dfrac{m v l}{2}\)
2 \(\dfrac{m v l}{2}+\dfrac{m l^{2}}{12} \omega\)
3 \(\dfrac{m l^{2} \omega}{12}\)
4 \(m v l\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365636 A sphere of mass \(M\) rolls without slipping on a rough surface with centre of mass has constant speed \(v_{0}\). If mass of the sphere is \(m\) and its radius be \(R\), then the angular momentum of the sphere about the point of contact is

1 \(-M v R(\hat{k})\)
2 \(\dfrac{5}{4} M v_{0} R(-\hat{k})\)
3 \(\dfrac{7}{5} M v_{0} R(-\hat{k})\)
4 \(\dfrac{9}{5} M v_{0} R(-\hat{k})\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365633 A particle performs uniform circular motion with an angular momentum \(L\). If the frequency of particle motion is doubled and its kinetic energy is halved, the angular momentum becomes

1 \(2 L\)
2 \(4 L\)
3 \(\dfrac{L}{2}\)
4 \(\dfrac{L}{4}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365634 A spherical body of mass \({m}\) and radius \({r}\) is released from rest along a smooth inclined plane of inclination \({\theta}\). The angular momentum of the body about the instantaneous point of contact after a time ' \({t}\) ' from the instant of release is

1 \({m g r t \cos \theta}\)
2 \({m g r t \sin \theta}\)
3 \({\dfrac{3}{2} m g r t \sin \theta}\)
4 None of these
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365635 A rod of mass \(m\) and length \(l\) is moving with linear velocity \(v\) and angular velocity \(\omega\). The angular momentum of the rod about point \(P\) is
supporting img

1 \(\dfrac{m v l}{2}\)
2 \(\dfrac{m v l}{2}+\dfrac{m l^{2}}{12} \omega\)
3 \(\dfrac{m l^{2} \omega}{12}\)
4 \(m v l\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365636 A sphere of mass \(M\) rolls without slipping on a rough surface with centre of mass has constant speed \(v_{0}\). If mass of the sphere is \(m\) and its radius be \(R\), then the angular momentum of the sphere about the point of contact is

1 \(-M v R(\hat{k})\)
2 \(\dfrac{5}{4} M v_{0} R(-\hat{k})\)
3 \(\dfrac{7}{5} M v_{0} R(-\hat{k})\)
4 \(\dfrac{9}{5} M v_{0} R(-\hat{k})\)