Explanation Given: The angular velocity ω C D of rod C D is 4 rad/s The angular velocity and position vector of rod C D are shown in Figure (1). Refer Figure (1): Write the expression for absolute velocity v C at point C in Cartesian vector from. v C = ω C D × r C / D (I). Write the angular velocity ω C D in Cartesian vector form. ω C D = ω C D k (II). Write the expression for position vector r C / D form D to C . r C / D = ( 0.5 j ) m Write the angular velocity ω B C in Cartesian vector form. ω B C = ω B C k The angular velocity, angle and position vector of rod A B are shown in Figure (2). Refer Figure (2): Write the expression for absolute velocity v B at point B in Cartesian vector from. v B = ω A B × r B / A (III). Write the angular velocity ω A B in Cartesian vector form. ω A B = ω A B k Write the expression for position vector r B / A form A to B . r B / A = ( 1 cos 30 ° i − 1 sin 30 ° j ) m The angular velocity, angle and position vector of rod B C are shown in Figure (3). Refer Figure (3): Write the expression for velocity of B relative to C in Cartesian vector form. v B = v C + ω B C × r B / C (IV). Write the expression for position vector r B / C form B to C . r B / C = ( − 0.4 i ) m Conclusion: Substitute 4 rad/s for ω C D in Equation (II). ω C D = 4 k Substitute ( 1 cos 30 ° i − 1 sin 30 ° j ) m for r B / A and ω A B k for ω A B in Equation (III). v B = ω A B × r B / A = ω A B k × ( 1 cos 30 ° i − 1 sin 30 ° j ) m = { ( 0.5 ω A B ) i + ( 0.866 ω A B ) j } m/s Substitute ( 0

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 16.6, Problem 87P

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The angular velocities of rods AB and CB

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Chapter 16.6, Problem 86P

Chapter 16.6, Problem 88P

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Engineering Mechanics: Statics & Dynamics (14th Edition)

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The angular velocities of rods A B and C B

Solution Summary: The author illustrates the angular velocity and position vector of rods AB and CB.

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The angular velocities of rods AB and CB

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Chapter 16 Solutions