Explanation Given: The radius and angular velocity is shown in Figure (1). The angular velocity is ω A = 40 ( t 3 + 6 t ) rad/s . Time t is 2 s . From Figure (1). The radius r A is 10 mm . The radius r B is 40 mm . The radius r E is 15 mm . Write the equation of the angular velocity. ω A = 40 ( t 3 + 6 t ) rad/s Here, angular velocity is ω . Write the expression for the angular acceleration of gear A . α A = d ω 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 ) . Write the expression for the angular acceleration of gear B . α B = d ω B d t (II) Here, angular acceleration is α and rate of change of angular velocity with respect to time is ( d ω d t ) . Write the velocity expression for the spindle E F . υ E = ω B r E (III) Here, velocity at point C is υ C , angular velocity is ω B and radius is r . Write the expression for tangential acceleration of the spindle E F . ( a t ) E = α B r E (IV) Here, tangential acceleration is a t , is radius of spindle E is r E and acceleration at B is α . Since, gear B is in mesh with gear A . Write the expression for normal acceleration of the spindle E F . ( a n ) E = ω B 2 r E (V) Here, normal acceleration is a n , is radius of spindle E is r E and angular velocity is ω . Conclusion: Substitute 40 ( t 3 + 6 t ) rad/s for ω A in Equation (I). α A = d d t 40 ( t 3 + 6 t ) = 40 ( 3 t 2 + 6 ) rad/s 2 Substitute 40 ( t 3 + 6 t ) rad/s for ω A , 10 mm for r A and 40 mm for r B in Equation (III). ω B = r A r B ω A = 10 40 ( 40 ( t 3 + 6 t ) ) (VI) Substitute 2 s for t in Equation (VI). ω B = 10 40 ( 40 ( t 3 + 6 t ) ) = 10 40 ( 40 ( ( 2 ) 3 + 6 ( 2 ) ) ) = 200 rad/s Substitute 10 40 ( 40 ( t 3 + 6 t ) ) for ω B in Equation (II)

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 16.3, Problem 34P

To determine

The magnitudes of the velocity and the tangential and normal components

of acceleration of the spindle EF when t is 2 s .

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Chapter 16.3, Problem 33P

Chapter 16.3, Problem 35P

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Engineering Mechanics: Statics & Dynamics (14th Edition)

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The magnitudes of the velocity and the tangential and normal components of acceleration of the spindle E F when t is 2 s .

Solution Summary: The author explains the magnitudes of the velocity and the tangential and normal components of acceleration in the spindle EF.

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The magnitudes of the velocity and the tangential and normal components

of acceleration of the spindle EF when t is 2 s .

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Chapter 16 Solutions

The magnitudes of the velocity and the tangential and normal components of acceleration of the spindle E F when t is 2 s .

Solution Summary: The author explains the magnitudes of the velocity and the tangential and normal components of acceleration in the spindle EF.

Concept explainers

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The magnitudes of the velocity and the tangential and normal components of acceleration of the spindle EF when t is 2 s .

Want to see the full answer?

Chapter 16 Solutions

The magnitudes of the velocity and the tangential and normal components

of acceleration of the spindle EF when t is 2 s .