A 56-kg dynamics instructor is demonstrating the principles of angular momentum to her class. She stands on a freely rotating platform with her body aligned with the vertical platform axis. With the platform not rotating, she holds a modified bicycle wheel so that its axis is vertical. She then turns the wheel axis 180° with respect to its initial vertical position without changing the 565-mm distance from the centerline of her body to the wheel center. The rim-weighted wheel has a mass of 14 kg and a centroidal radius of gyration of 325 mm and is spinning at a fairly constant rate of 247 rev/min. The instructor has a mass moment of inertia / = 3.57 kg-m² about the vertical platform axis. What rotational speed do the students observe with the wheel in this new position? 565 mm Answer: N = i ! rev/min

A 56-kg dynamics instructor is demonstrating the principles of angular momentum to her class. She stands on a freely rotating platform with her body aligned with the vertical platform axis. With the platform not rotating, she holds a modified bicycle wheel so that its axis is vertical. She then turns the wheel axis 180° with respect to its initial vertical position without changing the 565-mm distance from the centerline of her body to the wheel center. The rim-weighted wheel has a mass of 14 kg and a centroidal radius of gyration of 325 mm and is spinning at a fairly constant rate of 247 rev/min. The instructor has a mass moment of inertia / = 3.57 kg-m² about the vertical platform axis. What rotational speed do the students observe with the wheel in this new position? 565 mm Answer: N = i ! rev/min

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter10: Rotational Motion

Section: Chapter Questions

Problem 56P: A student sits on a freely rotating stool holding two dumbbells, each of mass 3.00 kg (Fig. P10.56)....

See similar textbooks

Similar questions

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 one of its ends. Find the magnitude of the rodsangular momentum.
The blades of a wind turbine are 30 m in length and rotate at a maximum rotation rate of 20 rev/min. (a) If the blades are 6000 kg each and the rotor assembly has three blades, calculate the angular momentum of the turbine at this rotation rate. (b) What Is the torque require to rotate the blades up to the maximum rotation rate in 5 minutes?
A solid cylinder of mass 2.0 kg and radius 20 cm is rotating counterclockwise around a vertical axis through its center at 600 rev/min. A second solid cylinder of the same mass and radius is rotating clockwise around the same vertical axis at 900 rev/min. If the cylinders couple so that they rotate about the same vertical axis, what is the angular velocity of the combination?
Two astronauts (Fig. P10.67), each having a mass M, are connected by a rope of length d having negligible mass. They are isolated in space, orbiting their center of mass at speeds v. Treating the astronauts as particles, calculate (a) the magnitude of the angular momentum of the two-astronaut system and (b) the rotational energy of the system. By pulling on the rope, one of the astronauts shortens the distance between them to d/2. (c) What is the new angular momentum of the system? (d) What are the astronauts new speeds? (e) What is the new rotational energy of the system? (f) How much chemical potential energy in the body of the astronaut was converted to mechanical energy in the system when he shortened the rope? Figure P10.67 Problems 67 and 68.
Find the net torque on the wheel in Figure P10.23 about the axle through O, taking a = 10.0 cm and b = 25.0 cm. Figure P10.23
The velocity of a particle of mass m = 2.00 kg is given by v= 5.10 + 2.40 m /s. What is the angular momentumof the particle around the origin when it is located atr= 8.60 3.70 m?
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.
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?
If the torque acting on a particle about an axis through a certain origin is zero, what can you say about its angular momentum about that axis?
Two astronauts (Fig. P10.67), each having a mass of 75.0 kg, are connected by a 10.0-m rope of negligible mass. They are isolated in space, orbiting their center of mass at speeds of 5.00 m/s. Treating the astronauts as particles, calculate (a) the magnitude of the angular momentum of the two-astronaut system and (b) the rotational energy of the system. By pulling on the rope, one astronaut shortens the distance between them to 5.00 m. (c) What is the new angular momentum of the system? (d) What are the astronauts new speeds? (e) What is the new rotational energy of the system? (f) How much chemical potential energy in the body of the astronaut was converted to mechanical energy in the system when he shortened the rope? Figure P10.67 Problems 67 and 68.
A wad of sticky clay with mass m and velocity vi is fired at a solid cylinder of mass M and radius R (Fig. P10.75). The cylinder is initially at rest and is mounted on a fixed horizontal axle that runs through its center of mass. The line of motion of the projectile is perpendicular to the axle and at a distance d R from the center. (a) Find the angular speed of the system just after the clay strikes and sticks to the surface of the cylinder. (b) Is the mechanical energy of the claycylinder system constant in this process? Explain your answer. (c) Is the momentum of the claycylinder system constant in this process? Explain your answer. Figure P10.75
A student sits on a freely rotating stool holding two dumbbells, each of mass 3.00 kg (Fig. P10.56). When his arms are extended horizontally (Fig. P10.56a), the dumbbells are 1.00 m from the axis of rotation and the student rotates with an angular speed of 0.750 rad/s. The moment of inertia of the student plus stool is 3.00 kg m2 and is assumed to be constant. The student pulls the dumbbells inward horizontally to a position 0.300 m from the rotation axis (Fig. P10.56b). (a) Find the new angular speed of the student. (b) Find the kinetic energy of the rotating system before and after he pulls the dumbbells inward. Figure P10.56