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 wo. After one revolution of the cylinder the rope has unwrapped and, at this instant, hangs vertically down, tangent to the cylinder. Part A Find the angular speed of the cylinder at this time. You can ignore the thickness of the rope. (Hint: Use Equation U = Mgyem ) Express your answer in terms of the variables m, M, R, wo, and the acceleration due to gravity g. Πνα ΑΣφ Part B

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 wo. After one revolution of the cylinder the rope has unwrapped and, at this instant, hangs vertically down, tangent to the cylinder. Part A Find the angular speed of the cylinder at this time. You can ignore the thickness of the rope. (Hint: Use Equation U = Mgyem ) Express your answer in terms of the variables m, M, R, wo, and the acceleration due to gravity g. Πνα ΑΣφ Part B

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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Concept explainers

Angular speed, acceleration and displacement

Angular acceleration is defined as the rate of change in angular velocity with respect to time. It has both magnitude and direction. So, it is a vector quantity.

Angular Position

Before diving into angular position, one should understand the basics of position and its importance along with usage in day-to-day life. When one talks of position, it’s always relative with respect to some other object. For example, position of earth with respect to sun, position of school with respect to house, etc. Angular position is the rotational analogue of linear position.

Question

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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 wo. After one
revolution of the cylinder the rope has unwrapped and, at this
instant, hangs vertically down, tangent to the cylinder.
Part A
Find the angular speed of the cylinder at this time. You can ignore the thickness of the rope. (Hint: Use Equation U = Mgyem -)
Express your answer in terms of the variables m, M, R, wo, and the acceleration due to gravity g.
| ν ΑΣφ
?
Part B
Find the linear speed of the lower end of the rope at this time.
Express your answer in terms of the variables m, M, R, wo, and the acceleration due to gravity g.
Hνα ΑΣφ
?
v =

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