01. Angular Displacement, Velocity and Acceleration
Rotational Motion

149837 If the length of the second's hand in a stopclock is \(3 \mathrm{~cm}\), the angular velocity and linear velocity of the tip is:

1 \(0.2047 \mathrm{rad} / \mathrm{s}, 0.0314 \mathrm{~ms}^{-1}\)
2 \(0.2547 \mathrm{rad} / \mathrm{s}, 0.314 \mathrm{~ms}^{-1}\)
3 \(0.1472 \mathrm{rad} / \mathrm{s}, 0.06314 \mathrm{~ms}^{-1}\)
4 \(0.1047 \mathrm{rad} / \mathrm{s}, 0.00314 \mathrm{~ms}^{-1}\)
5 \(0.347 \mathrm{rad} / \mathrm{s}, 0.314 \mathrm{~ms}^{-1}\)
Rotational Motion

149838 A motor is rotating at a constant angular velocity of \(500 \mathrm{rpm}\). The angular displacement per second is:

1 \(\frac{3}{50 \pi} \mathrm{rad}\)
2 \(\frac{3 \pi}{50} \mathrm{rad}\)
3 \(\frac{25 \pi}{3} \mathrm{rad}\)
4 \(\frac{3 \pi}{25} \mathrm{rad}\)
5 \(\frac{50 \pi}{3} \mathrm{rad}\)
Rotational Motion

149839 Two balls of mass \(m\) and \(4 m\) are connected by a rod of length \(L\). The mass of the rod is small and can be treated as zero. The size of the balls also can be neglected. We also assume the centre of the rod is hinged, but the rod can rotate about its centre in the vertical plane without friction. What is the gravity induced angular acceleration of the rod when the angle between the rod and the vertical line is \(\theta\) as shown.
original image

1 \(\frac{5 \mathrm{~g}}{6 \mathrm{~L}} \sin \theta\)
2 \(\frac{\mathrm{g}}{6 \mathrm{~L}} \cos \theta\)
3 \(\frac{6 \mathrm{~g}}{5 \mathrm{~L}} \sin \theta\)
4 \(\frac{\mathrm{g}}{3 \mathrm{~L}} \sin \theta\)
Rotational Motion

149840 A tire of radius \(R\) rolls on a flat surface with angular velocity \(\omega\) and velocity \(v\) as shown in the diagram. If \(v>\omega R\), in which direction does friction from the tire act on the road?

1 Towards downwar
2 Towards upwards
3 Towards the left
4 Towards the right
Rotational Motion

149837 If the length of the second's hand in a stopclock is \(3 \mathrm{~cm}\), the angular velocity and linear velocity of the tip is:

1 \(0.2047 \mathrm{rad} / \mathrm{s}, 0.0314 \mathrm{~ms}^{-1}\)
2 \(0.2547 \mathrm{rad} / \mathrm{s}, 0.314 \mathrm{~ms}^{-1}\)
3 \(0.1472 \mathrm{rad} / \mathrm{s}, 0.06314 \mathrm{~ms}^{-1}\)
4 \(0.1047 \mathrm{rad} / \mathrm{s}, 0.00314 \mathrm{~ms}^{-1}\)
5 \(0.347 \mathrm{rad} / \mathrm{s}, 0.314 \mathrm{~ms}^{-1}\)
Rotational Motion

149838 A motor is rotating at a constant angular velocity of \(500 \mathrm{rpm}\). The angular displacement per second is:

1 \(\frac{3}{50 \pi} \mathrm{rad}\)
2 \(\frac{3 \pi}{50} \mathrm{rad}\)
3 \(\frac{25 \pi}{3} \mathrm{rad}\)
4 \(\frac{3 \pi}{25} \mathrm{rad}\)
5 \(\frac{50 \pi}{3} \mathrm{rad}\)
Rotational Motion

149839 Two balls of mass \(m\) and \(4 m\) are connected by a rod of length \(L\). The mass of the rod is small and can be treated as zero. The size of the balls also can be neglected. We also assume the centre of the rod is hinged, but the rod can rotate about its centre in the vertical plane without friction. What is the gravity induced angular acceleration of the rod when the angle between the rod and the vertical line is \(\theta\) as shown.
original image

1 \(\frac{5 \mathrm{~g}}{6 \mathrm{~L}} \sin \theta\)
2 \(\frac{\mathrm{g}}{6 \mathrm{~L}} \cos \theta\)
3 \(\frac{6 \mathrm{~g}}{5 \mathrm{~L}} \sin \theta\)
4 \(\frac{\mathrm{g}}{3 \mathrm{~L}} \sin \theta\)
Rotational Motion

149840 A tire of radius \(R\) rolls on a flat surface with angular velocity \(\omega\) and velocity \(v\) as shown in the diagram. If \(v>\omega R\), in which direction does friction from the tire act on the road?

1 Towards downwar
2 Towards upwards
3 Towards the left
4 Towards the right
Rotational Motion

149837 If the length of the second's hand in a stopclock is \(3 \mathrm{~cm}\), the angular velocity and linear velocity of the tip is:

1 \(0.2047 \mathrm{rad} / \mathrm{s}, 0.0314 \mathrm{~ms}^{-1}\)
2 \(0.2547 \mathrm{rad} / \mathrm{s}, 0.314 \mathrm{~ms}^{-1}\)
3 \(0.1472 \mathrm{rad} / \mathrm{s}, 0.06314 \mathrm{~ms}^{-1}\)
4 \(0.1047 \mathrm{rad} / \mathrm{s}, 0.00314 \mathrm{~ms}^{-1}\)
5 \(0.347 \mathrm{rad} / \mathrm{s}, 0.314 \mathrm{~ms}^{-1}\)
Rotational Motion

149838 A motor is rotating at a constant angular velocity of \(500 \mathrm{rpm}\). The angular displacement per second is:

1 \(\frac{3}{50 \pi} \mathrm{rad}\)
2 \(\frac{3 \pi}{50} \mathrm{rad}\)
3 \(\frac{25 \pi}{3} \mathrm{rad}\)
4 \(\frac{3 \pi}{25} \mathrm{rad}\)
5 \(\frac{50 \pi}{3} \mathrm{rad}\)
Rotational Motion

149839 Two balls of mass \(m\) and \(4 m\) are connected by a rod of length \(L\). The mass of the rod is small and can be treated as zero. The size of the balls also can be neglected. We also assume the centre of the rod is hinged, but the rod can rotate about its centre in the vertical plane without friction. What is the gravity induced angular acceleration of the rod when the angle between the rod and the vertical line is \(\theta\) as shown.
original image

1 \(\frac{5 \mathrm{~g}}{6 \mathrm{~L}} \sin \theta\)
2 \(\frac{\mathrm{g}}{6 \mathrm{~L}} \cos \theta\)
3 \(\frac{6 \mathrm{~g}}{5 \mathrm{~L}} \sin \theta\)
4 \(\frac{\mathrm{g}}{3 \mathrm{~L}} \sin \theta\)
Rotational Motion

149840 A tire of radius \(R\) rolls on a flat surface with angular velocity \(\omega\) and velocity \(v\) as shown in the diagram. If \(v>\omega R\), in which direction does friction from the tire act on the road?

1 Towards downwar
2 Towards upwards
3 Towards the left
4 Towards the right
Rotational Motion

149837 If the length of the second's hand in a stopclock is \(3 \mathrm{~cm}\), the angular velocity and linear velocity of the tip is:

1 \(0.2047 \mathrm{rad} / \mathrm{s}, 0.0314 \mathrm{~ms}^{-1}\)
2 \(0.2547 \mathrm{rad} / \mathrm{s}, 0.314 \mathrm{~ms}^{-1}\)
3 \(0.1472 \mathrm{rad} / \mathrm{s}, 0.06314 \mathrm{~ms}^{-1}\)
4 \(0.1047 \mathrm{rad} / \mathrm{s}, 0.00314 \mathrm{~ms}^{-1}\)
5 \(0.347 \mathrm{rad} / \mathrm{s}, 0.314 \mathrm{~ms}^{-1}\)
Rotational Motion

149838 A motor is rotating at a constant angular velocity of \(500 \mathrm{rpm}\). The angular displacement per second is:

1 \(\frac{3}{50 \pi} \mathrm{rad}\)
2 \(\frac{3 \pi}{50} \mathrm{rad}\)
3 \(\frac{25 \pi}{3} \mathrm{rad}\)
4 \(\frac{3 \pi}{25} \mathrm{rad}\)
5 \(\frac{50 \pi}{3} \mathrm{rad}\)
Rotational Motion

149839 Two balls of mass \(m\) and \(4 m\) are connected by a rod of length \(L\). The mass of the rod is small and can be treated as zero. The size of the balls also can be neglected. We also assume the centre of the rod is hinged, but the rod can rotate about its centre in the vertical plane without friction. What is the gravity induced angular acceleration of the rod when the angle between the rod and the vertical line is \(\theta\) as shown.
original image

1 \(\frac{5 \mathrm{~g}}{6 \mathrm{~L}} \sin \theta\)
2 \(\frac{\mathrm{g}}{6 \mathrm{~L}} \cos \theta\)
3 \(\frac{6 \mathrm{~g}}{5 \mathrm{~L}} \sin \theta\)
4 \(\frac{\mathrm{g}}{3 \mathrm{~L}} \sin \theta\)
Rotational Motion

149840 A tire of radius \(R\) rolls on a flat surface with angular velocity \(\omega\) and velocity \(v\) as shown in the diagram. If \(v>\omega R\), in which direction does friction from the tire act on the road?

1 Towards downwar
2 Towards upwards
3 Towards the left
4 Towards the right
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