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Exactly one turn of a flexible rope with mass m is wrapped
Chapter 11, Problem 82P(choose chapter or problem)
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 ?0. 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. [?Hint: Use Eq. (9.18).]
Questions & Answers
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 ?0. 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. [?Hint: Use Eq. (9.18).]
ANSWER:Solution 82P Step 1 of 1: The zero of gravitational potential energy to be at the axle, the initial potential energy is zero (the rope is wrapped in a circle with center on the axle).When the rope has unwound, its center of mass is a distance R below th