Exactly one turn of a flexible rope with mass m is wrapped around a uniform cylinder with mass M and radius R. The cylinder rotates without friction about a horizontal axle along the cylinder axis. One end of the rope is attached to the cylinder. The cylinder starts with angular speed v0 . After one revolution of the cylinder the rope has unwrapped and, at this instant, hangs vertically down, tangent to the cylinder. Find the angular speed of the cylinder and the linear speed of the lower end of the rope at this time. Ignore the thickness of the rope.
Exactly one turn of a flexible rope with mass m is wrapped around a uniform cylinder with mass M and radius R. The cylinder rotates without friction about a horizontal axle along the cylinder axis. One end of the rope is attached to the cylinder. The cylinder starts with angular speed v0 . After one revolution of the cylinder the rope has unwrapped and, at this instant, hangs vertically down, tangent to the cylinder. Find the angular speed of the cylinder and the linear speed of the lower end of the rope at this time. Ignore the thickness of the rope.
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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Question
Exactly one turn of a flexible rope with mass m is wrapped
around a uniform cylinder with mass M and radius R. The cylinder rotates
without friction about a horizontal axle along the cylinder axis. One end
of the rope is attached to the cylinder. The cylinder starts with angular
speed v0 . After one revolution of the cylinder the rope has unwrapped
and, at this instant, hangs vertically down, tangent to the cylinder. Find the
angular speed of the cylinder and the linear speed of the lower end of the
rope at this time. Ignore the thickness of the rope.
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