Explanation Given: Centre of Mass G is located at a distance of 60 mm from geometric center C. Angular velocity of wheel various due to rolling of the wheel without sliding. Mass of wheel m = 3 k g Radius of wheel r = 180 m m Distance of G a n d C = 60 m m The radius of gyration, k = 90 m m Angular velocity = ω = 8 r a d / sec Concept used: Conservation of energy principle. Calculation: From the above figure, v 1 = ( B G ) ω 1 = ( 0.18 ) 2 + ( 0.06 ) 2 × 8 v 1 = 1.5178 m / s v 2 = 0.24 ω 2 Initial position 1: v 1 = 0 T 1 = 0 T 1 = m v 1 2 2 + I ω 1 2 2 = 3 To determine (b) Calculate the reaction at B at a horizontal surface when Centre of Mass G is exactly above the center of geometry C.

12th Edition

ISBN: 9781259977305

Author: BEER, Ferdinand P. (ferdinand Pierre), Johnston, E. Russell (elwood Russell), Cornwell, Phillip J., SELF, Brian P.

Publisher: Mcgraw-hill Education,

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Chapter 17.1, Problem 17.29P

To determine

(a)

Calculate the wheel’s angular velocity when mass center G of the wheel is exactly above the centre of Geometry C

To determine

(b)

Calculate the reaction at B at a horizontal surface when Centre of Mass G is exactly above the center of geometry C.

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Chapter 17.1, Problem 17.28P

Chapter 17.1, Problem 17.30P

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(a) Calculate the wheel’s angular velocity when mass center G of the wheel is exactly above the centre of Geometry C

Solution Summary: The author calculates the wheel's angular velocity when mass center G is exactly above the centre of Geometry C.