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Chapter Five – Circular Motion

In many cases object moves in a circular path,in that cases it is difficult for us to determine its direction. For this it is necessary to study circular motion.
Rate of change of angular displacement is angular velocity,and rate of change of angular velocity is angular acceleration.
Force required to move a body in a circular path is called centripetal force.
Product of moment of inertia and angular velocity is called angular momentum.
The objects that revolve around the earth due to gravity,are artificial satellites.the velocity required to put a satellite into its orbit around earth is called orbital velocity.

Q 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 * 10(8) m.

Q 5.2: A gramophone record turntable accelerate from rest to an angular velocity of 45.0 rev per min in 1.60 s. What is its average angular acceleration?

Q 5.3: A body of moment of inertia I = 0.80 kg m(2) about a fixed axis, rotates with constant angular velocity of 100 rad/s. Calculate its angular momentum L and the torque to sustain this motion.

Q 5.4: Consider the rotating cylinder shown in book figure 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 = 1/2mr(2)

Q 5.5: Calculate the angular momentum of a star of mass 2 * 10(30) kg and radius 7 * 10(5) Km. If it makes one complete rotation about its axis once in 20 days, what is its kinetic energy?

Q 5.6: A 1000 kg car traveling with a speed of 144 km/h rounds a curve of radius 100m. Find the necessary centripetal force.

Q 5.7: What is the least speed at which an aero plane 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?

Q 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 * …

Q 5.9: The earth rotates on its axis once a day. Suppose by some process the Earth contracts so that its radius is only half as large as at present. How fast will it be rotating then? (for sphere I = 2/5 MR(2)).

Q 5.10: What should be the orbiting speed to launch a satellite in a circular orbit 900km above the surface of the Earth? (Take mass of the Earth as 6 * 10(24) kg and its radius as 6400km).