## F.Sc ICS Notes: Physics XI: Chapter 5 Circular Motion Numerical Problems

__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 th beam? The distance of Moon from the Earth is 3.8 * 10(8) m.__

**Numerical Problem 5.1:**__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?__

**Numerical Problem 5.2:**__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.__

**Numerical Problem 5.3:**__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 = mr(2)/2__

**Numerical Problem 5.4:**__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?__

**Numerical Problem 5.5:**__A 1000 kg car traveling with a speed of 144 km/h rounds a curve of radius 100m. Find the necessary centripetal force.__

**Numerical Problem 5.6:**__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?__

**Numerical Problem 5.7:**__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 * 10(8)m. Radius of the Moon is 1.74 * 10(6)m.__

**Numerical Problem 5.8:**__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)).__

**Numerical Problem 5.9:**__What should be the orbiting speed to launch a satellite in a circular orbit 900km above the surface of the Earth (Me = 6 * 10(24)kg) and its radius 6400km.__

**Numerical Problem 5.10:**
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