Explanation Given: The angular velocity, ω = 6 rad / s . The angular acceleration, α = 10 rad / s 2 . The position vector directed from B to A , r B / A = 0 .75 m . The radial distance, r = 0.3 m . Conclusion: Express the linear velocity of collar B in the fixed system. v B = ( − ω × r B / A ) i (I) Substitute 6 rad / s for ω and 0 .3 m for r B / A in Equation (I). v B = ( − 6 × 0.3 ) i = { − 1.8 i } m / s Express the acceleration vector of collar B in the fixed system. a B = − α ( r B / A ) i − ω 2 ( r B / A ) j (II) Substitute 10 rad / s 2 for α , 6 rad / s for ω and 0 .3 m for r B / A in Equation (II). a B = − 10 ( 0.3 ) i − ( 6 ) 2 ( 0.3 ) j = { − 3 i − 10.8 j } m / s 2 Write the motion of moving reference. v A = 0 a A = 0 Ω = ω A C = ω A C k Ω ˙ = α A C = α A C k Here, acceleration vector of A is a A , angular velocity is Ω , angular acceleration is Ω ˙ , angular velocity of A C is ω A C and angular acceleration of A C is α A C . Write the motion of collar A with respect to moving reference. r B / A = { 0.75 i } m ( v A / B ) x y z = ( υ A / B ) x y z i ( a A / B ) x y z = ( a A / B ) i Apply the relative velocity equation. v B = v A + Ω × r B / A + ( v A / B ) x y z (III) Here, linear velocity of A is v A . Substitute { − 1.8 i } m / s for v B , 0 for v A , ω A C k for Ω , { 0.75 i } m for r B / A and ( υ A / B ) x y z i for ( v A / B ) x y z in Equation (III). − 1.8 i = 0 + ( ω A C k ) × ( 0.75 i ) + ( υ A / B ) x y z i = − ( υ A / B ) x y z i + ( 0.75 ω A C ) j (IV) Equate i component from Equation (IV). − 1.8 i = − ( υ A / B ) x y z i ( υ A / B ) x y z = 1

Engineering Mechanics: Dynamics; Modified Mastering Engineering with Pearson eText -- Standalone Access Card -- for Engineering Mechanics: Dynamics (14th Edition)

14th Edition

ISBN: 9780134229294

Author: HIBBELER

Publisher: PEARSON

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Chapter 16.8, Problem 151P

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The angular velocity ωAC and angular acceleration αAC of the slotted link AC .

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Chapter 16.8, Problem 150P

Chapter 16.8, Problem 152P

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Engineering Mechanics: Dynamics; Modified Mastering Engineering with Pearson eText -- Standalone Access Card -- for Engineering Mechanics: Dynamics (14th Edition)

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The angular velocity ω A C and angular acceleration α A C of the slotted link A C .

Solution Summary: The author analyzes the angular velocity of the slotted link AC and its acceleration. The position vector directed from BtoA.

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The angular velocity ωAC and angular acceleration αAC of the slotted link AC .

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Chapter 16 Solutions