The diameters of the main rotor and tail rotor of a single-engine helicopter are 7.56 m and 1.01 m, respectively. The respective rotational speeds are 457 rev/min and 4,130 rev/min. Calculate the speeds of the tips of both rotors. main rotor m/s m/s tail rotor Compare these speeds with the speed of sound, 343 m/s. Vmain rotor = Vsound sound = Vtail rotor

The diameters of the main rotor and tail rotor of a single-engine helicopter are 7.56 m and 1.01 m, respectively. The respective rotational speeds are 457 rev/min and 4,130 rev/min. Calculate the speeds of the tips of both rotors. main rotor m/s m/s tail rotor Compare these speeds with the speed of sound, 343 m/s. Vmain rotor = Vsound sound = Vtail rotor

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter12: Rotation I: Kinematics And Dynamics

Section: Chapter Questions

Problem 13PQ

See similar textbooks

Similar questions

A cam of mass M is in the shape of a circular disk of diameter 2R with an off-center circular hole of diameter R is mounted on a uniform cylindrical shaft whose diameter matches that of the hole (Fig. P1 3.78). a. What is the rotational inertia of the cam and shaft around the axis of the shaft? b. What is the rotational kinetic energy of the cam and shaft if the system rotates with angular speed around this axis?
Suppose when Earth was created, it was not rotating. However, after the application of a uniform torque after 6 days, it was rotating at 1 rev/day. (a) What was the angular acceleration during the 6 days? (b) What torque was applied to Earth during this period? (c) What force tangent to Earth at its equator would produce this torque?
A uniform disk of mass M = 3.00 kg and radius r = 22.0 cm is mounted on a motor through its center. The motor accelerates the disk uniformly from rest by exerting a constant torque of 1.00 Nm. a. What is the time required for the disk to reach an angular speed of 8.00 102 rpm? b. What is the number of revolutions through which the disk spins before reaching this angular speed?
A wheel 1.0 m in diameter rotates with an angular acceleration of 4.0rad/s2 . (a) If the wheel’s initial angular velocity is 2.0 rad/s, what is its angular velocity after 10 s? (b) Through what angle does it rotate in the 10-s interval? (c) What are the tangential speed and acceleration of a point on the rim of the wheel at the end of the 10-s interval?
A disk is initially at rest. A penny is placed on it at a distance of 1.0 m from the rotation axis. At time t = 0 s, the disk begins to rotate with a constant angular acceleration of 2.0 rad/s2 around a fixed, vertical axis through its center and perpendicular to its plane. Find the magnitude of the net acceleration of the coin at t = 1.5 s.
A centrifuge used for training astronauts rotating at 0.810 rad/s is spun up to 1.81 rad/s with an angular acceleration of 0.050 rad/s2. a. What is the magnitude of the angular displacement that the centrifuge rotates through during this increase in speed? b. If the initial and final speeds of the centrifuge were tripled and the angular acceleration remained at 0.050 rad/s2, what would be the factor by which the result in part (a) would change?
The motion of spinning a hula hoop around one's hips can bemodeled as a hoop rotating around an axis not through the center, but offset from the center by an amount h, where h is lessthan R, the radius of the hoop. Suppose Maria spins a hula hoopwith a mass of 0.75 kg and a radius of 0.62 m around her waist.The rotation axis is perpendicular to the plane of the hoop, butapproximately 0.40 m from the center of the hoop. a. What isthe rotational inertia of the hoop in this case? b. If the hula hoopis rotating with an angular speed of 13.7 rad/s, what is its rotational kinetic energy?
Lara is running just outside the circumference of a carousel, looking for her favorite horse to ride, with a constant angular speed of 1.00 rad/s. Just as she spots the horse, one-fourth of the circumference ahead of her, the carousel begins to move, accelerating from rest at 0.050 rad/s2. a. Taking the time when the carousel begins to move as t = 0, when will Lara catch up to the horse? b. Lara mistakenly passes the horse and keeps running at constant angular speed. If the carousel continues to accelerate at the same rate, when will the horse draw even with Lara again?
Problems 62 and 63 are paired. 62. C A disk is rotating around a fixed axis that passes through its center and is perpendicular to the face of the disk. Consider a point on the rim of the disk (point R) and another point halfway between the center and the rim (point H) at one particular instant. a. How does the angular speed v of the disk at point H compare with the angular speed of the disk at point R? b. How does the tangential speed of the disk at point H compare with the tangential speed of the disk at point R? c. Suppose we pick a point H on the disk at random (by throwing a dart, for example), and we compare the speeds at that point with the speeds at point R. How will the answers to parts (a) and (b) be different? Explain.
A long, thin rod of mass m = 5.00 kg and length = 1.20 m rotates around an axis perpendicular to the rod with an angularspeed of 3.00 rad/s. a. What is the angular momentum of therod if the axis passes through the rods midpoint? b. What is theangular momentum of the rod if the axis passes through a pointhalfway between its midpoint and its end?
A ceiling fan is rotating counterclockwise with a constant angular acceleration of rad/s2 about a fixed axis perpendicular to its plane and through its center. Assume the fan starts from rest. a. What is the angular velocity of the fan after 4.0 s? b. What is the angular displacement of the fan after 4.0 s? c. How many revolutions has the fan gone through in 4.0 s?
Consider again the two wind turbines in Problem 32. a. At what point along the 40-m blade would the angular distance traveled by the point be the same as the angular distance traveled by the point at the end of the 20-m blade? b. At what point along the 40-m blade would the translational distance traveled by the point be the same as the translational distance traveled by the point at the end of the 20-m blade?