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qUESTIONS

1.Rotational Dynamics

Somehow, an ant is stuck to the rim of a bicycle wheel of diameter 1 m. While the bicycle is on a central stand, the wheel is set into rotation and it attains the frequency of 2 rev/s in 10 seconds, with uniform angular acceleration. Calculate (i) Number of revolutions completed by the ant in these 10 seconds. (ii) Time taken by it for first complete revolution and the last complete revolution.

1.Rotational Dynamics

A ceiling fan having moment of inertia 2 kg-m2 attains its maximum frequency of 60 rpm in ‘2π’ seconds. Calculate its power rating.

1.Rotational Dynamics

A spherical water balloon is revolving at 60 rpm. In the course of time, 48.8 % of its water leaks out. With what frequency will the remaining balloon revolve now? Neglect all non-conservative forces.

1.Rotational Dynamics

A tiny stone of mass 20 g is tied to a practically massless, inextensible, flexible string and whirled along vertical circles. Speed of the stone is 8 m/s when the centripetal force is exactly equal to the force due to the tension. Calculate minimum and maximum kinetic energies of the stone during the entire circle. Let θ = 0 be the angular position of the string, when the stone is at the lowermost position. Determine the angular position of the string when the force due to tension is numerically equal to weight of the stone.

1.Rotational Dynamics

Semi-vertical angle of the conical section of a funnel is 370. There is a small ball kept inside the funnel. On rotating the funnel, the maximum speed that the ball can have in order to remain in the funnel is 2 m/s. Calculate inner radius of the brim of the funnel. Is there any limit upon the frequency of rotation? How much is it? Is it lower or upper limit? Give a logical reasoning. (Use g = 10 m/s2 and sin 370 = 0.6)

1.Rotational Dynamics

A merry-go-round usually consists of a central vertical pillar. At the top of it there are horizontal rods which can rotate about vertical axis. At the end of this horizontal rod there is a vertical rod fitted like an elbow joint. At the lower end of each vertical rod, there is a horse on which the rider can sit. As the merry-go-round is set into rotation, these vertical rods move away from the axle by making some angle with the vertical.

1.Rotational Dynamics

A racing track of curvature 9.9 m is banked at tan−1 0.5 . Coefficient of static friction between the track and the tyres of a vehicle is 0.2. Determine the speed limits with 10 % margin.

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