4) The diameters of the main rotor and tail rotor of a single engine helicopter

Question

4) The diameters of the main rotor and tail rotor of a single engine helicopter are 7.6 meters and 1.02 meters respectively. The respective rotational speed are 450 rev/min and 4,138 rev/min. (a) Calculate the angular speed of both rotors. (b) Calculate the tangential (linear) speed of the tips of both rotors. ANS: 47.1 rad/s & 433.3 rad/s; (b) 358 m/s & 442 m/s An electric motor rotating a workshop grinding wheel at a rate of 100 rev/min is switched off. Assume the wheel has a constant negative angular acceleration of magnitude of 2 rad/s'. (a) Find the angular speed of the wheel in radians/second. (b) How long does it take for the grinding wheel to stop? (c) Through how many radians has the wheel turned during the interval found in part (b)? ANS: 10.5 rad/s; (b) 5.25 s; (c) 27.6 rads 5) A 0.4 kg object attached to the end of a string of length of 0.5 meter is swung in a circular path and in a horizontal plane. If a constant angular speed of 8 rad/s is maintained, what is the (a) tangential (inear) speed of the object, and (b) the tension in the string? ANS: (a) 4 m/s; (b) 12.8 N 6) A 50 kg child stands at the rim of a merry-go-round of radius 2 meters, rotating with an angular sped of 3 rad (a) What is the child's tangential (linear) speed? (b) What is the child's centripetal acceleration? (c) What provides the force between her feet and the floor? (d) What is the force between her feet and the floor of the carousel? ANS: 6 m/s; (b) 18 m/s; (c) Friction (d) 900 N 7) Two children are on a carousel. The girl is on a horse located 1.5 meters from the center of the carousel, and the boy is located on a horse 3 meters from the center of the carousel. The girl is spinning at a rate a 2 rev/min. (a) Determine the angular velocity of the boy in rev/min. (b) Determine the angular speed of the girl in radians/sec. (c) Determine the angular speed of the boy in radians/sec. 8) d the tangential (linear) velocity of the boy. ANS: (a) 2 rev/min; (b) 0.21 rad/s; (c) 0.21 rad/s; (d) 0.315 m/s; (e) 0.63 m/s

Explanation / Answer

I will solve only one full question at one time.

4) One rotation of tip of main rotor = 7.6m * pi = 23.88 m
450 * 23.88 = 10746 m/minute
10746/ 60 seconds per minute = 179.1 m/s

One rotation of tip of tail rotor = 1.02m * pi = 3.2 m
4138* 3.2 = 13241.6 m/minute
13241.6/ 60 seconds per minute = 220.7 m/s

main rotor = 179.1 m/s
tail rotor = 220.7 m/s

Angular speed of main rotor = 179.1/3.8 = 47.1 rad/s

Angular speed of tail rotor = 220.7/0.51 = 432.75 rad/s

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