Question 4: An annulus of inner and outer radii Rị and R2 has a non-uniform surface mass density given by o = 0or where o is a positive constant and r is the radial distance from the origin (radial coordinate in the cylindrical coordinates) as shown in Figure 2. a) Find the moment of inertia of the rod about an axis passing through its center of mass (the origin). Express your result in terms of M (mass of the annulus) and R1 and R2. b) Check your result as R1 - 0 and R2 = R.

Question 4: An annulus of inner and outer radii Rị and R2 has a non-uniform surface mass density given by o = 0or where o is a positive constant and r is the radial distance from the origin (radial coordinate in the cylindrical coordinates) as shown in Figure 2. a) Find the moment of inertia of the rod about an axis passing through its center of mass (the origin). Express your result in terms of M (mass of the annulus) and R1 and R2. b) Check your result as R1 - 0 and R2 = R.

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)...

See similar textbooks

Similar questions

Pls answer i will rate if answered quickly
Q1
Need help with this homework question. Thank you!
Suppose we want to calculate the moment of inertia of a 65.5 kg skater, relative to a vertical axis through their center of mass. a. First calculate the moment of inertia (in kg⋅m2) when the skater has their arms pulled inward by assuming they are cylinder of radius 0.125 m. b. Now calculate the moment of inertia of the skater (in kg⋅m2) with their arms extended by assuming that each arm is 5% of the mass of their body. Assume the body is a cylinder of the same size, and the arms are 0.875 m long rods extending straight out from the center of their body being rotated at the ends.
Consider a rotating disk of radius R that has the exotic property that it can change its massper unit area as a function of r. Initially, its mass per unit area is given by ar3, where a is aconstant. What is the moment of inertia of this disk expressed in terms of its mass, M andradius R.
hi please solve
Please as soon as possible
Find the center of mass and the moment of inertia about the y-axis for a thin rectangular plate cut from the first quadrant by the lines x= 6 and y =1 if 8(x,y) = 3x +y +5. (..... What are the coordinates of the center of mass? (Type an integer or a simplified fraction.)
A uniform solid sphere of mass 6.0 kg and radius 10 cm is rolling without slipping along a horizontal surface with a speed of 4.9 m/s (this is the speed of the center of mass) when it starts up a ramp that makes an angle of 30° with the horizontal. 1st а) b) While the ball is moving up the ramp, find What is the maximum distance it can go up the ramp, measured along the surface of the ramp? 2nd? the acceleration (magnitude and direction) of its center of mass and i) ii) | 3rd 3] the friction force (magnitude and direction) acting on it due to the surface of the ramp. Moment of inertia of a solid sphere is I em =MR². ст
A wheel consists of a thin hoop (mass .20 kg, radius .5m) and 4 spikes (each having a mass of .05kg, length .5m) and is constrained to rotate about its center. There are three forces acting on the wheel: 5N at the outer edge, 3N halfway between the center and the outer edge, and 1N at the center. 1. Find the momentum of inertia of the wheel 2. find the anguar acceleration of the wheel