Explanation Given information: The radius of cylinder is r . The weight of the cylinder is W . The initial counterclockwise angular velocity of disk is ω 0 . The coefficient of kinetic friction between the cylinder and the wall and the floor μ k . Calculation: Write the general equation of the mass ( m ) of the disk. W = m g m = W g Write the equation of moment of inertia cylinder ( I ¯ ) : I ¯ = 1 2 m r 2 Substitute W g for m . I ¯ = 1 2 ( W g ) r 2 = W r 2 2 g Consider principle of impulse and momentum. Syst Momenta 1 + Syst Ext Imp 1 → 2 = Syst Momenta 2 Sketch the impulse and momentum diagram as shown in Figure (1). Refer Figure (1). Write the general equation of frictional force ( F A ) between floor and the disk. F A = μ k N A (1) Here, N A is the normal force on the disk by the floor. Write the general equation of frictional force ( F B ) between vertical wall and the disk. F B = μ k N B (2) Here, N B is the normal force on the disk by the vertical wall. Consider the horizontal linear momentum. 0 + N B t − F A t = 0 N B = F A Here, t is the time required for the cylinder to come to rest. Consider the vertical linear momentum. 0 + N A t + F B t − W t = 0 N A + F B = W Substitute μ k N B for F B . N A + μ k N B = W Substitute F A for N B . N A + μ k ( F A ) = W Substitute μ k N A for N A . N A + μ k ( μ k N A ) = W N A ( 1 + μ k 2 ) = W N A = W 1 + μ k 2 Find the equation of frictional force ( F A ) between floor and the disk using Equation (1): F A = μ k N A Substitute W 1 + μ k 2 for N A . F A = μ k W 1 + μ k 2 Find the equation of frictional force ( F B ) between vertical wall and the disk using Equation (2): F B = μ k N B Substitute F A for N B

Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9780073398242

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Chapter 17.2, Problem 17.59P

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Derive an expression for the time required for the cylinder to come to rest.

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Chapter 17 Solutions

Vector Mechanics for Engineers: Statics and Dynamics

Ch. 17.1 - A round object of mass m and radius r is released...Ch. 17.1 - Prob. 17.2CQ Ch. 17.1 - Prob. 17.3CQ Ch. 17.1 - Prob. 17.4CQ Ch. 17.1 - Slender bar A is rigidly connected to a massless...Ch. 17.1 - A 200-kg flywheel is at rest when a constant 300...Ch. 17.1 - The rotor of an electric motor has an angular...Ch. 17.1 - Prob. 17.3P Ch. 17.1 - Two disks of the same material are attached to a...Ch. 17.1 - Prob. 17.5P

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Derive an expression for the time required for the cylinder to come to rest.

Solution Summary: The author illustrates the equation of moment of inertia of a cylinder.

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