Problem 9: The rotor blades of a helicopter are rotating at a constant angular velocity of 6.0 rad/s. Consider the motion of the tip of a blade, which sits at a radius of 5m from the rotor axis. (a) What are the 5m magnitudes of the tip velocity and acceleration? (b) If an angular acceleration of 6.0 rad/s is applied to the rotor, determine the initial magnitude of the tip acceleration, and the angle the acceleration vector makes with the rotor blade. Ans. (a) v-30 m/s, a-180.0 m/s², (b) a-182.5 m/s², 039.46° * = moderately difficult ** = for experts

Problem 9: The rotor blades of a helicopter are rotating at a constant angular velocity of 6.0 rad/s. Consider the motion of the tip of a blade, which sits at a radius of 5m from the rotor axis. (a) What are the 5m magnitudes of the tip velocity and acceleration? (b) If an angular acceleration of 6.0 rad/s is applied to the rotor, determine the initial magnitude of the tip acceleration, and the angle the acceleration vector makes with the rotor blade. Ans. (a) v-30 m/s, a-180.0 m/s², (b) a-182.5 m/s², 039.46° * = moderately difficult ** = for experts

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter8: Rotational Equilibrium And Dynamics

Section: Chapter Questions

Problem 47P: The uniform thin rod in Figure P8.47 has mass M = 3.50 kg and length L = 1.00 m and is free to...

See similar textbooks

Similar questions

A uniform rod of length b stands vertically upright on a rough floor and then tips over. What is the rods angular velocity when it hits the floor?
A disk 8.00 cm in radius rotates at a constant rate of 1200 rev/min about its central axis. Determine (a) its angular speed in radians per second, (b) the tangential speed at a point 3.00 cm from its center, (c) the radial acceleration of a point on the rim, and (d) the total distance a point on the rim moves in 2.00 s.
In testing an automobile tire for proper alignment, a technicianmarks a spot on the tire 0.200 m from the center. He then mountsthe tire in a vertical plane and notes that the radius vector to thespot is at an angle of 35.0 with the horizontal. Starting from rest,the tire is spun rapidly with a constant angular acceleration of 3.00 rad/s2. a. What is the angular speed of the wheel after 4.00 s? b. What is the tangential speed of the spot after 4.00 s? c. What is the magnitude of the total accleration of the spot after 4.00 s?" d. What is the angular position of the spot after 4.00 s?
Jeff, running outside to play, pushes on a swinging door, causing its motion to be briefly described by = t2 + 0.800 t + 2.00,where t is in seconds and is in radians. At t = 0 and at t = 1.50s, what are the a. angular position, b. angular speed, and c. angularacceleration of the door?
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?
A digital audio compact disc carries data, each bit of which occupies 0.6 m along a continuous spiral track from the inner circumference of the disc to the outside edge. A CD player turns the disc to carry the track counterclockwise above a lens at a constant speed of 1.30 m/s. Find the required angular speed (a) at the beginning of the recording, where the spiral has a radius of 2.30 cm, and (b) at the end of the recording, where the spiral has a radius of 5.80 cm. (c) A full-length recording lasts for 74 min 33 s. Find the average angular acceleration of the disc. (d) Assuming that the acceleration is constant, find the total angular displacement of the disc as it plays. (e) Find the total length of the track.
The propeller of an aircraft accelerates from rest with an angular acceleration = 4t + 6, where is in rad/s2 and t isin seconds. What is the angle in radians through which thepropeller rotates from t = 1.00 s to t = 6.00 s?
Why is the following situation impossible? Starting from rest, a disk rotates around a fixed axis through an angle of 50.0 rad in a time interval of 10.0 s. The angular acceleration of the disk is constant during the entire motion, and its final angular speed is 8.00 rad/s.
A space station is coast me ted in the shape of a hollow ring of mass 5.00 104 kg. Members of the crew walk on a deck formed by the inner surface of the outer cylindrical wall of the ring, with radius r = 100 m. At rest when constructed, the ring is set rotating about its axis so that the people inside experience an effective free-fall acceleration equal to g. (Sec Fig. P11.29.) The rotation is achieved by firing two small rockets attached tangentially to opposite points on the rim of the ring, (a) What angular momentum does the space station acquirer (b) For what time interval must the rockets be fired if each exerts a thrust of 125 N?
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 point on a rotating turntable 20.0 cm from the center accelerates from rest to a final speed of 0.700 m/s in 1.75 s. At t = 1.25 s, find the magnitude and direction of (a) the radial acceleration, (b) the tangential acceleration, and (c) the total acceleration of the point.
A thin rod of length 2.65 m and mass 13.7 kg is rotated at anangular speed of 3.89 rad/s around an axis perpendicular to therod and through its center of mass. Find the magnitude of therods angular momentum.