Explanation Given: The constant angular velocity of the rod A B (moving reference)is Ω = 3 rad/s (counter clock wise). The angle θ = 30 ° . Draw the free body diagram of system as shown in Figure 1. Refer Figure (1). Write the formula for velocity of the point C measured from the x , y , z reference. v C = v A + Ω × r C / A + ( v C / A ) x y z (I) Here, v C velocity vector of point C measured from the X , Y , Z reference, v A is the velocity vector of the origin A measured from the X , Y , Z reference, ( v C / A ) x y z is the velocity vector of point C with respect to rod end A measured by an observer attached to the rotating x , y , z reference, Ω is the angular velocity of the x , y , z reference measured from the X , Y , Z reference and r C / A is the position vector of the point C with respect to rod end A . Conclusion: Refer Figure (1). Consider the rod A B as the moving reference x y z . Here, the moving reference doesn’t have displacement, it revolves along z − a x i s . The linear velocity of the moving reference x y z becomes zero. v A = 0 The vector coordinate of angular velocity of the moving reference x y z is Ω = 3 k Refer Figure (1). Consider the triangle O C O ' . cos 60 ° = O O ' 0.4 m O O ' = 0.4 cos 60 ° O O ' = 0.2 m Consider the triangle A C O ' . cos 30 ° = A O + O O ' r r = 0.4 m + 0.2 m cos 30 ° r = 0.6 m 0.8660 r = 0.6928 m Refer Figure (1). Write the position vector ( r C / A ) directed from A to C . r C / A = ( 0.6928 cos 30 ° ) i + ( 0.6928 sin 30 ° ) j = 0 .6i + 0.3464 j Refer Figure (1). Calculate the vector coordinate of the velocity ( v C ) at point C . v C = − ( v C cos 30 ° ) i + ( v C sin 30 ° ) j = − 0.866 v C i + 0.5 v C j Calculate the relative velocity of the point C with respect to the point A (moving reference). ( v C / A ) x y z = ( v C / A cos 30 ° ) i + ( v C / A sin 30 ° ) j = 0 .866 v C / A i + 0

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 16.8, Problem 135P

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The velocity of point C when θ=30° .

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Chapter 16.8, Problem 134P

Chapter 16.8, Problem 136P

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The velocity of point C when θ = 30 ° .

Solution Summary: The author explains the formula for velocity of the point C measured from the x,y,z reference.

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