To determine The instantaneous velocity and acceleration of point B . Explanation Write the expression for the instantaneous velocity of point B . v B = r × ω (I) Here, instantaneous velocity of point B is v B , angular velocity of the device is ω and position vector of point B is r . Write the expression for the instantaneous acceleration of point B . a B = α × r + ω × ( r × ω ) (II) Here, instantaneous acceleration of point B is a B and angular acceleration of the device is α . Conclusion: Write the angular velocity of the device in vector form using the right hand rule. ω = 20 k rad / s Here, unit vector along z -direction is k . Write the angular acceleration of the device in vector form using the right hand rule. α = − 40 k rad / s 2 Write the position vector for distance between the points O and A . r O A = O A ¯ j (III) Here, distance between the points O and A is O A ¯ and unit vector along y -direction is j . Substitute 300 mm for O A ¯ in Equation (III). r O A = ( 300 mm ) j = 300 j mm = 0.3 j m Write the position vector for distance between the points A and B . r A B = A B ¯ ( cos 60 ° j + sin 60 ° k ) (IV) Here, distance between the points A and B is A B ¯ . Substitute 500 mm for A B ¯ in Equation (IV). r A B = ( 500 mm ) ( cos 60 ° j + sin 60 ° k ) = ( 0 .5 m ) ( cos 60 ° j + sin 60 ° k ) = 0.25 j + 0.433 k m Calculate the position vector of point B . r = r O A + r A B Substitute 0.3 j m for r O A and 0.25 j + 0.433 k m for r A B . r = ( 0.3 j m ) + ( 0.25 j + 0.433 k m ) = 0.55 j + 0

8th Edition

ISBN: 9781118885840

Author: James L. Meriam, L. G. Kraige, J. N. Bolton

Publisher: WILEY

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Chapter 5.2, Problem 11P

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The instantaneous velocity and acceleration of point B.

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Engineering Mechanics: Dynamics

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