Rotational Motion of Rigid Body
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366074 A ceiling fan is rotating around a fixed axle as shown. The direction of angular velocity is along
supporting img

1 \({+\hat{j}}\)
2 \({-\hat{j}}\)
3 \({+\hat{k}}\)
4 \({-\hat{k}}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366075 Two points \(A\) and \(B\) on a disc have velocities \(v_{1}\) and \(v_{2}\) respectively, at some moment. Their directions make angles \(60^{\circ}\) and \(30^{\circ}\), respectively, with the line of separation as shown in the figure. The angular velocity of disc is \((A\)and \(B\) are seperated by \('d'\))
supporting img

1 \(\dfrac{v_{2}}{\sqrt{3} d}\)
2 \(\dfrac{v_{2}}{d}\)
3 \(\dfrac{v_{2}-v_{1}}{d}\)
4 \(\dfrac{\sqrt{3} v_{1}}{d}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366076 Two end points of a rod move with velocities \(3 v\) and \(v\) perpendicular to the rod and in the same direction, separated by a distance ' \(r\) '. Then the angular velocity of the rod is

1 \(\dfrac{2 v}{r}\)
2 \(\dfrac{3 v}{r}\)
3 \(\dfrac{4 v}{r}\)
4 \(\dfrac{5 v}{r}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366077 Two particles \(A\) and \(B\) are situated at a distance \(d = 2\;m\) apart. Particle \(A\) has a velocity of \(10\;m/s\) at an angle of \(60^{\circ}\) and particle \(B\) has velocity \(v\) at an angle \(30^{\circ}\) as shown in the figure. The distance \(\mathrm{d}\) between \(A\) and \(B\) is constant. The angular velocity of \(B\) with respect to \(A\) is:
supporting img

1 \(\dfrac{5}{\sqrt{3}} \mathrm{rad} / \mathrm{s}\)
2 \(\dfrac{10}{\sqrt{3}} \mathrm{rad} / \mathrm{s}\)
3 \(5 \sqrt{3} \mathrm{rad} / \mathrm{s}\)
4 \(10 \sqrt{3} \mathrm{rad} / \mathrm{s}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366078 A solid cylinder of mass \(2\;kg\) and radius \(4\;cm\) is rotating about its axis at the rate of \(3\,rpm\). The torque required to stop after \(2 \pi\) revolutions is

1 \(2 \times {10^{ - 6}}\;N\;m\)
2 \(2 \times {10^{ - 3}}\;N\;m\)
3 \(12 \times {10^{ - 4}}\;N\;m\)
4 \(2 \times {10^6}\;N\;m\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366074 A ceiling fan is rotating around a fixed axle as shown. The direction of angular velocity is along
supporting img

1 \({+\hat{j}}\)
2 \({-\hat{j}}\)
3 \({+\hat{k}}\)
4 \({-\hat{k}}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366075 Two points \(A\) and \(B\) on a disc have velocities \(v_{1}\) and \(v_{2}\) respectively, at some moment. Their directions make angles \(60^{\circ}\) and \(30^{\circ}\), respectively, with the line of separation as shown in the figure. The angular velocity of disc is \((A\)and \(B\) are seperated by \('d'\))
supporting img

1 \(\dfrac{v_{2}}{\sqrt{3} d}\)
2 \(\dfrac{v_{2}}{d}\)
3 \(\dfrac{v_{2}-v_{1}}{d}\)
4 \(\dfrac{\sqrt{3} v_{1}}{d}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366076 Two end points of a rod move with velocities \(3 v\) and \(v\) perpendicular to the rod and in the same direction, separated by a distance ' \(r\) '. Then the angular velocity of the rod is

1 \(\dfrac{2 v}{r}\)
2 \(\dfrac{3 v}{r}\)
3 \(\dfrac{4 v}{r}\)
4 \(\dfrac{5 v}{r}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366077 Two particles \(A\) and \(B\) are situated at a distance \(d = 2\;m\) apart. Particle \(A\) has a velocity of \(10\;m/s\) at an angle of \(60^{\circ}\) and particle \(B\) has velocity \(v\) at an angle \(30^{\circ}\) as shown in the figure. The distance \(\mathrm{d}\) between \(A\) and \(B\) is constant. The angular velocity of \(B\) with respect to \(A\) is:
supporting img

1 \(\dfrac{5}{\sqrt{3}} \mathrm{rad} / \mathrm{s}\)
2 \(\dfrac{10}{\sqrt{3}} \mathrm{rad} / \mathrm{s}\)
3 \(5 \sqrt{3} \mathrm{rad} / \mathrm{s}\)
4 \(10 \sqrt{3} \mathrm{rad} / \mathrm{s}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366078 A solid cylinder of mass \(2\;kg\) and radius \(4\;cm\) is rotating about its axis at the rate of \(3\,rpm\). The torque required to stop after \(2 \pi\) revolutions is

1 \(2 \times {10^{ - 6}}\;N\;m\)
2 \(2 \times {10^{ - 3}}\;N\;m\)
3 \(12 \times {10^{ - 4}}\;N\;m\)
4 \(2 \times {10^6}\;N\;m\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366074 A ceiling fan is rotating around a fixed axle as shown. The direction of angular velocity is along
supporting img

1 \({+\hat{j}}\)
2 \({-\hat{j}}\)
3 \({+\hat{k}}\)
4 \({-\hat{k}}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366075 Two points \(A\) and \(B\) on a disc have velocities \(v_{1}\) and \(v_{2}\) respectively, at some moment. Their directions make angles \(60^{\circ}\) and \(30^{\circ}\), respectively, with the line of separation as shown in the figure. The angular velocity of disc is \((A\)and \(B\) are seperated by \('d'\))
supporting img

1 \(\dfrac{v_{2}}{\sqrt{3} d}\)
2 \(\dfrac{v_{2}}{d}\)
3 \(\dfrac{v_{2}-v_{1}}{d}\)
4 \(\dfrac{\sqrt{3} v_{1}}{d}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366076 Two end points of a rod move with velocities \(3 v\) and \(v\) perpendicular to the rod and in the same direction, separated by a distance ' \(r\) '. Then the angular velocity of the rod is

1 \(\dfrac{2 v}{r}\)
2 \(\dfrac{3 v}{r}\)
3 \(\dfrac{4 v}{r}\)
4 \(\dfrac{5 v}{r}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366077 Two particles \(A\) and \(B\) are situated at a distance \(d = 2\;m\) apart. Particle \(A\) has a velocity of \(10\;m/s\) at an angle of \(60^{\circ}\) and particle \(B\) has velocity \(v\) at an angle \(30^{\circ}\) as shown in the figure. The distance \(\mathrm{d}\) between \(A\) and \(B\) is constant. The angular velocity of \(B\) with respect to \(A\) is:
supporting img

1 \(\dfrac{5}{\sqrt{3}} \mathrm{rad} / \mathrm{s}\)
2 \(\dfrac{10}{\sqrt{3}} \mathrm{rad} / \mathrm{s}\)
3 \(5 \sqrt{3} \mathrm{rad} / \mathrm{s}\)
4 \(10 \sqrt{3} \mathrm{rad} / \mathrm{s}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366078 A solid cylinder of mass \(2\;kg\) and radius \(4\;cm\) is rotating about its axis at the rate of \(3\,rpm\). The torque required to stop after \(2 \pi\) revolutions is

1 \(2 \times {10^{ - 6}}\;N\;m\)
2 \(2 \times {10^{ - 3}}\;N\;m\)
3 \(12 \times {10^{ - 4}}\;N\;m\)
4 \(2 \times {10^6}\;N\;m\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366074 A ceiling fan is rotating around a fixed axle as shown. The direction of angular velocity is along
supporting img

1 \({+\hat{j}}\)
2 \({-\hat{j}}\)
3 \({+\hat{k}}\)
4 \({-\hat{k}}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366075 Two points \(A\) and \(B\) on a disc have velocities \(v_{1}\) and \(v_{2}\) respectively, at some moment. Their directions make angles \(60^{\circ}\) and \(30^{\circ}\), respectively, with the line of separation as shown in the figure. The angular velocity of disc is \((A\)and \(B\) are seperated by \('d'\))
supporting img

1 \(\dfrac{v_{2}}{\sqrt{3} d}\)
2 \(\dfrac{v_{2}}{d}\)
3 \(\dfrac{v_{2}-v_{1}}{d}\)
4 \(\dfrac{\sqrt{3} v_{1}}{d}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366076 Two end points of a rod move with velocities \(3 v\) and \(v\) perpendicular to the rod and in the same direction, separated by a distance ' \(r\) '. Then the angular velocity of the rod is

1 \(\dfrac{2 v}{r}\)
2 \(\dfrac{3 v}{r}\)
3 \(\dfrac{4 v}{r}\)
4 \(\dfrac{5 v}{r}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366077 Two particles \(A\) and \(B\) are situated at a distance \(d = 2\;m\) apart. Particle \(A\) has a velocity of \(10\;m/s\) at an angle of \(60^{\circ}\) and particle \(B\) has velocity \(v\) at an angle \(30^{\circ}\) as shown in the figure. The distance \(\mathrm{d}\) between \(A\) and \(B\) is constant. The angular velocity of \(B\) with respect to \(A\) is:
supporting img

1 \(\dfrac{5}{\sqrt{3}} \mathrm{rad} / \mathrm{s}\)
2 \(\dfrac{10}{\sqrt{3}} \mathrm{rad} / \mathrm{s}\)
3 \(5 \sqrt{3} \mathrm{rad} / \mathrm{s}\)
4 \(10 \sqrt{3} \mathrm{rad} / \mathrm{s}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366078 A solid cylinder of mass \(2\;kg\) and radius \(4\;cm\) is rotating about its axis at the rate of \(3\,rpm\). The torque required to stop after \(2 \pi\) revolutions is

1 \(2 \times {10^{ - 6}}\;N\;m\)
2 \(2 \times {10^{ - 3}}\;N\;m\)
3 \(12 \times {10^{ - 4}}\;N\;m\)
4 \(2 \times {10^6}\;N\;m\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366074 A ceiling fan is rotating around a fixed axle as shown. The direction of angular velocity is along
supporting img

1 \({+\hat{j}}\)
2 \({-\hat{j}}\)
3 \({+\hat{k}}\)
4 \({-\hat{k}}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366075 Two points \(A\) and \(B\) on a disc have velocities \(v_{1}\) and \(v_{2}\) respectively, at some moment. Their directions make angles \(60^{\circ}\) and \(30^{\circ}\), respectively, with the line of separation as shown in the figure. The angular velocity of disc is \((A\)and \(B\) are seperated by \('d'\))
supporting img

1 \(\dfrac{v_{2}}{\sqrt{3} d}\)
2 \(\dfrac{v_{2}}{d}\)
3 \(\dfrac{v_{2}-v_{1}}{d}\)
4 \(\dfrac{\sqrt{3} v_{1}}{d}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366076 Two end points of a rod move with velocities \(3 v\) and \(v\) perpendicular to the rod and in the same direction, separated by a distance ' \(r\) '. Then the angular velocity of the rod is

1 \(\dfrac{2 v}{r}\)
2 \(\dfrac{3 v}{r}\)
3 \(\dfrac{4 v}{r}\)
4 \(\dfrac{5 v}{r}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366077 Two particles \(A\) and \(B\) are situated at a distance \(d = 2\;m\) apart. Particle \(A\) has a velocity of \(10\;m/s\) at an angle of \(60^{\circ}\) and particle \(B\) has velocity \(v\) at an angle \(30^{\circ}\) as shown in the figure. The distance \(\mathrm{d}\) between \(A\) and \(B\) is constant. The angular velocity of \(B\) with respect to \(A\) is:
supporting img

1 \(\dfrac{5}{\sqrt{3}} \mathrm{rad} / \mathrm{s}\)
2 \(\dfrac{10}{\sqrt{3}} \mathrm{rad} / \mathrm{s}\)
3 \(5 \sqrt{3} \mathrm{rad} / \mathrm{s}\)
4 \(10 \sqrt{3} \mathrm{rad} / \mathrm{s}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366078 A solid cylinder of mass \(2\;kg\) and radius \(4\;cm\) is rotating about its axis at the rate of \(3\,rpm\). The torque required to stop after \(2 \pi\) revolutions is

1 \(2 \times {10^{ - 6}}\;N\;m\)
2 \(2 \times {10^{ - 3}}\;N\;m\)
3 \(12 \times {10^{ - 4}}\;N\;m\)
4 \(2 \times {10^6}\;N\;m\)