Explanation Given: The relative velocity of the block with respect to moving reference is v A / O = 2 m/s . The relative acceleration of the block with respect to moving reference is a A / O = 4 m/s 2 . The constant angular velocity of the fork (moving reference)is Ω = 4 rad/s . Draw the free body diagram of system as shown in Figure 1. Refer Figure (1). Write the formula for acceleration of the block measured from the x , y , z reference a A = a O + Ω ˙ × r A / O + Ω × ( Ω × r A / O ) + 2 Ω × ( v A / O ) x y z + ( a A / O ) x y z (I) Here, a A acceleration vector of block A measured from the X , Y , Z reference, a O is the acceleration vector of the origin measured from the X , Y , Z reference, ( v A / O ) x y z , ( a A / O ) x y z is the velocity and acceleration vector of the block A with respect to hole O measured by an observer attached to the rotating x , y , z reference, Ω ˙ is the angular acceleration due to the rotation of x , y , z reference, Ω is the angular velocity of the x , y , z reference measured from the X , Y , Z reference and r A / O is the position vector of the block A with respect to hole O . Conclusion: Refer Figure (1). Consider the fork 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 and acceleration of the moving reference x y z becomes zero. v O = 0 a O = 0 The vector coordinate of angular velocity of the moving reference x y z is Ω = 4 k Since, the moving reference x y z revolves with constant speed. Hence the angular acceleration becomes zero. Ω ˙ = 0 Refer Figure (1). Consider the block A . Write the position vector ( r A / O ) directed from O to A . r A / O = 0.1 i + 0 j = 0 .1i Refer Figure (1). The vector coordinate for the relative velocity of the block with respect to moving reference is ( v A / O ) x y z = − 2 i . The vector coordinate for the relative acceleration of the block with respect to moving reference is ( a A / O ) x y z = − 4 i

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Author: HIBBELER

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Chapter 16, Problem 134P

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The acceleration of the block A at the instant shown.

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Chapter 16, Problem 133P

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The acceleration of the block A at the instant shown.

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