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Problem 2 (6 points): Consider a cylinder of mass m and radius r, to roll without slip on the surface of the fixed half-cylinder. If the cylinder (of mass moment of inertia lG = nmr?, wheren is a variable that takes on values based on whether the cylinder of mass m is a particle (n = 0) or à rigid body (n > 0)), is initially at the top of the half-cylinder, änd is then given an infinitesimal nudge down the half-cylinder, a) Determine, for a general value of n, the equation of motion for the rolling cylinder during the time it is in contact with the half-cylinder. b) At what angle will the cylinder lose contact with the half-cylinder? Your answer will be in terms of the variable n. c) Now, for n= 0, n = 0.5, n = 1, and n= 2/5, determine the angle of separation from the half-cylinder surface. e =0 at roll with- release out slip Re /R

Problem 2 (6 points): Consider a cylinder of mass m and radius r, to roll without slip on the surface of the fixed half-cylinder. If the cylinder (of mass moment of inertia lG = nmr?, wheren is a variable that takes on values based on whether the cylinder of mass m is a particle (n = 0) or à rigid body (n > 0)), is initially at the top of the half-cylinder, änd is then given an infinitesimal nudge down the half-cylinder, a) Determine, for a general value of n, the equation of motion for the rolling cylinder during the time it is in contact with the half-cylinder. b) At what angle will the cylinder lose contact with the half-cylinder? Your answer will be in terms of the variable n. c) Now, for n= 0, n = 0.5, n = 1, and n= 2/5, determine the angle of separation from the half-cylinder surface. e =0 at roll with- release out slip Re /R

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Problem 2 (6 points): Consider a cylinder of mass m and radius r, to roll without slip on the surface of the fixed half-cylin
Problem 2 (6 points): Consider a cylinder of mass m and radius r, to roll without slip on the surface of the fixed half-cylinder. If the cylinder (of mass moment of inertia lG = nmr2, wheren is a variable that takes on values based on whether the cylinder of mass m is a particle (n 0) or a rigid body (n > 0)), is initially at the top of the half-cylinder, and is then given an infinitesimal nudge down the half-cylinder, a) Determine, for a general value of n, the equation of motion for the rolling cylinder during the time it is in contact with the half-cylinder. b) At what angle will the cylinder lose contact with the half-cylinder? Your answer will be in terms of the variable n. !! c) Now, for n= 0, n = 0.5, n= 1, and n = 2/5, determine the angle of separation from the half-cylinder surface. e = 0 at %3D roll with- release out slip R
Transcribed Image Text:Problem 2 (6 points): Consider a cylinder of mass m and radius r, to roll without slip on the surface of the fixed half-cylinder. If the cylinder (of mass moment of inertia lG = nmr2, wheren is a variable that takes on values based on whether the cylinder of mass m is a particle (n 0) or a rigid body (n > 0)), is initially at the top of the half-cylinder, and is then given an infinitesimal nudge down the half-cylinder, a) Determine, for a general value of n, the equation of motion for the rolling cylinder during the time it is in contact with the half-cylinder. b) At what angle will the cylinder lose contact with the half-cylinder? Your answer will be in terms of the variable n. !! c) Now, for n= 0, n = 0.5, n= 1, and n = 2/5, determine the angle of separation from the half-cylinder surface. e = 0 at %3D roll with- release out slip R
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