To determine The acceleration of point D for the position shown. Explanation Write the expression for the velocity of point A in vector form. v A = v B + r A / B × ω A B (I) Here, velocity of point A in vector form is v A , velocity of point B in vector form is v B , position vector of point A with respect to point A is r A / B and angular velocity of the link AB in vector form is ω A B . Write the expression for the acceleration of point A in vector form. a A = a B + α A B × r A / B − ( ω A B ) 2 r A / B (II) Here, acceleration of point A in vector form is a A , acceleration of point B in vector form is a B and angular acceleration of the link AB in vector form is α A B . Write the expression for the acceleration of point D in vector form. a D = a A + α A B × r D / A − ( ω A B ) 2 r D / A (III) Here, acceleration of point D in vector form is a D and position vector of point D with respect to point A is r D / A . Conclusion: Write the angular velocity of the link AB in vector form using right hand rule. ω A B = ω A B k rad / s Here, unit vector along z direction is k . Write the position vector of point A with respect to point B . r A / B = − 0.30 sin 45 ° i + 0.30 cos 45 ° j m Here, unit vectors along x and y -directions are i and j respectively. Write the velocities of points A and B in vector form using right hand rule. v A = ( 0.50 m / s ) j = 0.50 j m / s v B = v B i m / s Substitute 0.50 j m / s for v A , v B i m / s for v B , − 0.30 sin 45 ° i + 0.30 cos 45 ° j m for r A / B and ω A B k rad / s for ω A B in Equation (I). 0.50 j m / s = ( v B i m / s ) + ( − 0.30 sin 45 ° i + 0.30 cos 45 ° j m ) × ( ω A B k rad / s ) 0.50 j = v B i − 0.2121 ω A B i − 0.2121 ω A B j (IV) Compare coefficients of j in Equation (IV). 0.50 = − 0.2121 ω A B ω A B = − 2.357 rad / s Compare coefficients of i in Equation (IV). v B − 0.2121 ω A B = 0 Substitute − 2.357 rad / s for ω A B . v B − 0.2121 ( − 2.357 rad / s ) = 0 v B = − 0.5 m / s Write the angular acceleration of the link AB in vector form using right hand rule

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ISBN: 9781119047315

Author: Bolton

Publisher: VST

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Chapter 5.6, Problem 150P

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The acceleration of point D for the position shown.

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Chapter 5.6, Problem 149P

Chapter 5.6, Problem 151P

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EBK ENGINEERING MECHANICS: DYNAMICS, SI

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