Explanation Given: The angular velocity, radius of the pulley and wheel is shown in Figure (1). The angular acceleration is α A is 30 rad/s 2 . From Figure (1) the radius r A is 200 mm . From Figure (1) the radius r B is 125 mm . Time t is 3 s . Write the expression for the angular velocity. ω A = ( ω 0 ) A + α c t (I) Here, angular velocity ω , is angular acceleration is α c and time is t . Write the expression angular velocity ω B of pulley B and ω A of Wheel A . ω A r A = ω B r B ω B = r A r B ω A (II) Here, angular velocity of Wheel A is ω A , angular velocity of pulley B is ω B , radius of pulley B is r B and radius of Wheel A is r A . Write the expression angular acceleration α B of pulley B and α A of Wheel A . α A r A = α B r B α B = r A r B α A (III) Here, angular acceleration of Wheel A is α A , angular acceleration of pulley B is α B , radius of pulley B is r B and radius of Wheel A is r A . Write the expression of tangential acceleration. ( a P ) t = α B r B (IV) Here, tangential acceleration is ( a P ) t , angular acceleration is α and radius is r A . Write the expression of normal acceleration. ( a P ) n = ω B 2 r B (V) Here, normal acceleration is ( a P ) n , angular velocity is ω and radius is r A . Conclusion: Substitute 30 rad/s 2 for α , 0 for ω 0 and 3 s for t in Equation (I)

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 16.3, Problem 32P

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The tangential and normal acceleration of point located at the rim B when time t is 3 s .

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Engineering Mechanics: Statics & Dynamics (14th Edition)

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The tangential and normal acceleration of point located at the rim B when time t is 3 s .

Solution Summary: The author shows the angular velocity, radius of the pulley and wheel in Figure (1).

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The tangential and normal acceleration of point located at the rim B when time t is 3 s .

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