Explanation Given: Radius of the bend is r = 220 mm and point B is moved to a distance 20 mm . Concept used: By applying torque method for the given system is expressed as follows: T i + T e = 0 ...... (1) Here, inertial torque of the system is T i and external torque is T e . Calculation: Let the wire with uniform linear density ρ . Mass of the bend is expressed as follows: m = ρ ( 2 r + π r ) Distance C is calculated as follows: m g c = π ρ r ( 2 r π ) g c = 2 r 2 ρ ρ ( 2 r + π r ) c = 2 r 2 + π Moment of inertia of the bend is calculated as follows: I = I semi circle + I linear I = m semi circle r 2 + m linear ( 2 r ) 2 12 I = ρ × π r × r 2 + ρ × 2 r × 4 r 2 12 I = m r 2 ( 2 + π ) ( π + 2 3 ) From above figure torque is expressed as: T i + T e = I θ ¨ + m g c θ Substitute I θ ¨ + m g c θ for T i + T e in equation (1)

Vector Mechanics for Engineers: Dynamics

11th Edition

ISBN: 9780077687342

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

Publisher: McGraw-Hill Education

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Chapter 19.2, Problem 19.62P

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The velocity at B.

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The velocity at B.

Solution Summary: The author calculates the moment of inertia of the bend by applying torque method for the given system.

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