Nonuniform cylindrical object. In the figure, a cylindrical object of mass M and radius R rolls smoothly from rest down a ramp and onto ahorizontal section. From there it rolls off the ramp and onto the floor, landing a horizontal distance d = 0.470 m from the end of theramp. The initial height of the object is H = 0.92 m; the end of the ramp is at height h = 0.13 m. The object consists of an outercylindrical shell (of a certain uniform density) that is glued to a central cylinder (of a different uniform density). The rotational inertia ofthe object can be expressed in the general form | = ßMR², but ẞ is not 0.5 as it is for a cylinder of uniform density. Determine ẞ.HNumberUnitshT

It appears to be a voltage divider circuit with a dependent current source. Here's a breakdown of…

Answered: Nonuniform cylindrical object. In the…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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A solid disk rotates in the horizontal plane at an angular velocity of 0.042 rad/s with respect to an axis perpendicular to the disk at its center. The moment of inertia of the disk is 0.089 kg·m2. From above, sand is dropped straight down onto this rotating disk, so that a thin uniform ring of sand is formed at a distance 0.29 m from the axis. The sand in the ring has a mass of 0.42 kg. After all the sand is in place, what is the angular velocity of the disk?
A carousel has a radius of 1.70 m and a moment of inertia of 118 kg m2. A girl of mass 47.5 kg is standing at the edge of the carousel, which is rotating with an angular speed of 3.10 rad/s. Now the girl walks toward the center of the carousel and stops at a certain distance from the center d. The angular speed of the carousel is now 5.2 rad/s. How far from the center, in meters, did the girl stop?
A thin rod has a length of 0.537 m and rotates in a circle on a frictionless tabletop. The axis is perpendicular to the length of the rod at one of its ends. The rod has an angular velocity of 0.778 rad/s and a moment of inertia of 1.10 x 10³ kg-m². A bug standing on the axis decides to crawl out to the other end of the rod. When the bug (whose mass is 5 x 10-3 kg) gets where it's going, what is the change in the angular velocity of the rod?
A cylinder of radius 1.84 cm1.84 cm and a spherical shell of radius 9.47 cm9.47 cm are rolling without slipping along the same floor. The two objects have the same mass. If they are to have the same total kinetic energy, what should the ratio of the cylinder's angular speed to the spherical shell's angular speed be?
A ball (in the form of a spherical shell which has a moment of inertia of 2/3 M R^2) rolls down a roof, then falls to the ground. The ball has a mass of 1.65 g and a radius of 15.0 cm. The roof is inclined at 20.0 degrees and the ball rolls a distance of 3 meters along the roof before falling off. a) What is the angular speed of the ball at the moment it leaves the roof? b) If the distance from the end of the roof to the ground is 2.50 m, how many revolutions does the ball make before it hits the ground?
A girl of mass 31.8 kg stands on the rim of a frictionless merry-go-round of radius 1.63 m and rotational inertia 313 kg-m2 that is not moving. She throws a rock of mass 948 g horizontally in a direction that is tangent to the outer edge of the merry-go-round. The speed of the rock, relative to the ground, is 3.26 m/s. Afterward, what are (a) the angular speed of the merry-go-round and (b) the linear speed of the girl? (a) Number i Units (b) Number i Units
A cylinder has a cone removed from it. The cylinder and the conical hole have the same radius (2.06 meters) and height (4.56 meters). The cylinder has a density of 447 kg/m3. What is the rotational inertia of the cylinder with the cone removed in kg m2? You can set your origin at the tip of the cone, which is also the center of the base of the cylinder.
A hollow sphere (I=\frac{2}{3}mr^2I=32mr2) of radius R rotates about a diameter with an angular speed \omegaω. The sphere then collapses (magically) under the action of internal forces to a final radius of R/2 with no change in its mass. What is the final angular speed of the sphere?
A thin stick of mass 0.2 kg and length L = 0.5 m is attached to the rim of a metal disk of mass M = 2.0 kg and radius R = 0.3 m . The stick is free to rotate around a horizontal axis through its other end (see the following figure). (a) If the combination is released with the stick horizontal, what is the speed of the center of the disk when the stick is vertical? (b) What is the acceleration of the center of the disk at the instant the stick is released? (c) At the instant the stick passes through the vertical?
A thin rod has a length of 0.792 m and rotates in a circle on a frictionless tabletop. The axis is perpendicular to the length of the rod at one of its ends. The rod has an angular velocity of 0.939 rad/s and a moment of inertia of 1.41 x 103 kg-m². A bug standing on the axis decides to crawl out to the other end of the rod. When the bug (whose mass is 5 x 10-³ kg) gets where it's going, what is the change in the angular velocity of the rod?
A flat uniform circular disk (radius = 6.22 m, mass=320 kg) is initially stationary. The disk is free to rotate in the horizontal plane about a frictionless axis perpendicular to the center of the disk. A 51.0-kg person, standing 2.32 m from the axis, begins to run on the disk in a circular path and has a tangential speed of 3.00 m/s relative to the ground. Find the resulting angular speed (in rad/s) of the disk.
A solid sphere is released from the top of a ramp that is at a height h, = 1.85 m. It rolls down the ramp without slipping. The bottom of the ramp is at a height of h, = 1.48 m above the floor. The edge of the ramp is a short horizontal section from which the ball leaves to land on the floor. The diameter of the ball is 0.12 m. h2 (a) Through what horizontal distance d, in meters, does the ball travel before landing? (b) How many revolutions does the ball make during its fall? rev

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