Numerical Problems 5.1: A tiny laser beam is directed from the Earth to the Moon. If the beam is to have a diameter of 2.50 m at the Moon, how small must divergence angle be for the beam? The distance of Moon from the Earth is 3.8 ｘ10⁸ m. (Ans: 6.6ｘ10⁻⁹ rad)

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Numerical Problems 5.3: A body of moment of inertia I = 0.80 kg m² about a fixed axis, rotates with constant angular velocity of 100 rad s⁻¹. Calculate its angular momentum L and the torque to sustain this motion. (Ans: 80 Js, 0)

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Numerical Problems 5.4: Consider the rotating cylinder shown in Fid 5.26. Suppose that m= 5 kg, F = 0.60 N and r = 0.20 m. Calculate (a) the torque acting on the cylinder, (b) the angular acceleration of the cylinder.(Moment of inertia of cylinder = `\frac {1}{2}`mr² 

(Ans: 0.12 N, 12 rad s⁻¹)

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Numerical Problems 5.5: Calculate the angular momentum of a star of mass 2 ï½˜10³⁰ kg and radius 7 ï½˜ 10⁵ Km. If it makes one complete rotation about its axis once in 20 days, what is its kinetic energy? (Ans: 14ｘ10⁴² J s,  2.5 ｘ10³⁶ J)

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Numerical Problems 5.6: A 1000 kg car traveling with a speed of 144 km h⁻¹ rounds a curve of radius 100 m. Find the necessary centripetal force. (Ans: 1.6 ｘ10⁴ N)

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Numerical Problems 5.7: What is the least speed at which an aeroplane can execute a vertical loop of 1 km radius so that there will be no tendency for the pilot to fall down at the highest point? (Ans: 99 m s⁻¹)

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Numerical Problems 5.8: The moon orbits the Earth so that the same side always faces the Earth. Determine the ratio of its spin angular momentum (about its own axis) and its orbital angular momentum. (In this case, treat the Moon as a particle orbiting the Earth). Distance between the Earth and the Moon is 3.85 ｘ10⁸ m. Radius of the Moon is 1.74 ï½˜10⁶ m. (Ans: 8.2 ｘ10⁻⁶)

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