The figure shows a rigid assembly of a thin hoop (of mass m = 0.28 kg and radius R = 0.13 m) and a thin radial rod (of length L = 2R and also of mass m = 0.28 kg). The assembly is upright, but we nudge it so that it rotates around a horizontal axis in the plane of the rod and hoop, through the lower end of the rod. Assuming that the energy given to the assembly in the nudge is negligible, what is the assembly's angular speed about the rotation axis when it passes through the upside-down (inverted) orientation?

The figure shows a rigid assembly of a thin hoop (of mass m = 0.28 kg and radius R = 0.13 m) and a thin radial rod (of length L = 2R and also of mass m = 0.28 kg). The assembly is upright, but we nudge it so that it rotates around a horizontal axis in the plane of the rod and hoop, through the lower end of the rod. Assuming that the energy given to the assembly in the nudge is negligible, what is the assembly's angular speed about the rotation axis when it passes through the upside-down (inverted) orientation?

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 cylindrical grinding wheel of mass 50.0 kg and diameter 1.0 m is turned on by an electric motor. The friction in the bearings is negligible. (a) What torque must be applied to the wheel to bring it from rest to 120 rev/min in 20 revolutions? (b) A tool whose coefficent of kinetic friction with the wheel with a force of 40.0 N. What torque must be supplied by the motor to keep the wheel rotating at a constant angular velocity?
An electric sander consisting of a rotating disk of mass 0.7 kg and radius 10 cm rotates at 15 rev/sec. When applied to a rough wooden wall the rotation rate decreases by 20 . (a) What is the final rotational kinetic energy of the rotating disk? (a) How much has its rotational kinetic energy decreased?
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
Consider the disk in Problem 71. The disks outer rim hasradius R = 4.20 m, and F1 = 10.5 N. Find the magnitude ofeach torque exerted around the center of the disk. FIGURE P12.71 Problems 71-75
The uniform thin rod in Figure P8.47 has mass M = 3.50 kg and length L = 1.00 m and is free to rotate on a friction less pin. At the instant the rod is released from rest in the horizontal position, find the magnitude of (a) the rods angular acceleration, (b) the tangential acceleration of the rods center of mass, and (c) the tangential acceleration of the rods free end. Figure P8.47 Problems 47 and 86.
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?
Review. A small object with mass 4.00 kg moves counterclockwise with constant angular speed 1.50 rad/s in a circle of radius 3.00 m centered at the origin. It starts at the point with position vector 3.00im. It then undergoes an angular displacement of 9.00 rad. (a) What is its new position vector? Use unit-vector notation for all vector answers. (b) In what quadrant is the particle located, and what angle does its position vector make with the positive x axis? (c) What is its velocity? (d) In what direction is it moving? (e) What is its acceleration? (f) Make a sketch of its position, velocity, and acceleration vectors. (g) What total force is exerted on the object?
A square plate with sides 2.0 m in length can rotatearound an axle passingthrough its center of mass(CM) and perpendicular toits surface (Fig. P12.53). There are four forces acting on the plate at differentpoints. The rotational inertia of the plate is 24 kg m2. Use the values given in the figure to answer the following questions. a. Whatis the net torque acting onthe plate? b. What is theangular acceleration of the plate? FIGURE P12.53 Problems 53 and 54.
Review. An object with a mass of m = 5.10 kg is attached to the free end of a light string wrapped around a reel of radius R = 0.250 m and mass M = 3.00 kg. The reel is a solid disk, free to rotate in a vertical plane about the horizontal axis passing through its center as shown in Figure P10.29. The suspended object is released from rest 6.00 m above the floor. Determine (a) the tension in the string, (b) the acceleration of the object, and (c) the speed with which the object hits the floor. (d) Verify your answer to part (c) by using the isolated system (energy) model. Figure P10.29
An approximate model for a ceiling fan consists of a cylindrical disk with four thin rods extending from the disks center, as in Figure P8.41. The disk has mass 2.50 kg and radius 0.200 m. Each rod has mass 0.850 kg and is 0.750 m long, (a) Find the ceiling fans moment of inertia about a vertical axis through the disks center, (b) Friction exerts a constant torque of magnitude 0.115 N m on the fan as it rotates. Find the magnitude of the constant torque provided by the fans motor if the fan starts from rest and takes 15.0 s and 18.5 full revolutions to reach its maximum speed. Figure P8.41
The angular momentum vector of a precessing gyroscope sweeps out a cone as shown in Figure P11.31. The angular speed of the tip of the angular momentum vector, called its precessional frequency, is given by p=/I, where is the magnitude of the torque on the gyroscope and L is the magnitude of its angular momentum. In the motion called precession of the equinoxes, the Earths axis of rotation processes about the perpendicular to its orbital plane with a period of 2.58 104 yr. Model the Earth as a uniform sphere and calculate the torque on the Earth that is causing this precession. Figure P11.31 A precessing angular momentum vector sweeps out a cone in space.
Given the disk and density in Problem 11, derive an expression for the rotational inertia of this disk around an axis at theedge of the disk and perpendicular to the disks surface.