Explanation Given: The gears A , B and radius of gears are shown in Figure (1). The angular acceleration α A is ( 4 t 3 ) rad/s 2 . The angular velocity ( ω A ) 0 is 20 rad/s . The radius of the gear A is 0.05 m . The radius of the gear B is 0.15 m . The time t is 2 s . Write the expression for the angular acceleration. α A = d ω A d t d ω A = α A d t (I) Here, angular acceleration is α and rate of change of angular velocity with respect to time is ( d ω d t ) . Since, gear B is in mesh with gear A . Write the expression angular velocity ω B of gear B and ω A of gear A . ω A r A = ω B r B ω B = r A r B ω A (II) Here, angular velocity of gear A is ω A , angular velocity of gear B is ω B , radius of gear B is r B and radius of gear A is r A . Conclusion: Substitute ( 4 t 3 ) rad/s 2 for α in Equation (I). Integrate the Equation (I) at the limits 20 rad/s to ω A for ω and 0 to 2 s for t

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 16.3, Problem 20P

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The angular velocity ωB of gear B when time t is 2 s .

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Chapter 16.3, Problem 19P

Chapter 16.3, Problem 21P

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Chapter 16 Solutions

Engineering Mechanics: Statics & Dynamics (14th Edition)

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The angular velocity ω B of gear B when time t is 2 s .

Solution Summary: The angular velocity and radius of gears are shown in Figure (1).

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The angular velocity ωB of gear B when time t is 2 s .

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