Explanation Given: Therelativevelocity of the ball with respect to disk (moving reference)is ( v B / O ) x y z = 600 mm/s . The relative acceleration of the ball with respect to disk (moving reference) is ( a B / O ) x y z = 150 mm/s 2 . The angular velocity of the disk(moving reference)is Ω = 6 rad/s . The angular acceleration of the disk (moving reference)is Ω ˙ = 3 rad/s 2 . Draw the free body diagram of the system as shown in Figure (1). Write the formula for velocity of the ball measured from the x , y , z reference. v B = v O + Ω × r B / O + ( v B / O ) x y z (I) Here, v B velocity vector of ball measured from the X , Y , Z reference, v O is the velocity vector of the origin O measured from the X , Y , Z reference, ( v B / O ) x y z is the velocity vector of ball with respect to origin O 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 B / O is the position vector of the ball with respect to origin O . Write the formula for acceleration of the ball measured from the x , y , z reference a B = a O + Ω ˙ × r B / O + Ω × ( Ω × r B / O ) + 2 Ω × ( v B / O ) x y z + ( a B / O ) x y z (II) Here, a B is the acceleration vector of ball measured from the X , Y , Z reference, a O is the acceleration vector of the origin measured from the X , Y , Z reference, ( v B / O ) x y z , ( a B / O ) x y z is the velocity and acceleration vector of the ballwith respect to origin 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 B / O is the position vector of the ball with respect to origin O . Conclusion: Refer Figure (1). Consider the disk 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 = ( 6 k ) rad/s The vector coordinate of angular acceleration of the moving reference x y z is Ω ˙ = ( 3 k ) rad/s 2 Refer Figure (1). Consider the ball. Write the position vector ( r B / O ) directed from origin to ball. r B / O = 0.4 i + 0 j = 0.4 i Refer Figure (1). The vector coordinate for the relative velocity of the ball with respect to moving reference is ( v B / O ) x y z = ( 600 mm/s × 1 m 1000 mm ) i + 0 j = ( 0 .6i ) m/s The vector coordinate for the relative acceleration of the ball with respect to moving reference is ( a B / O ) x y z = ( 150 mm/s 2 × 1 m 1000 mm ) i + 0 j = ( 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 129P

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The velocity and acceleration of the ball at the instant.

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Chapter 16.8, Problem 128P

Chapter 16.8, Problem 130P

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Chapter 16 Solutions

Engineering Mechanics: Statics & Dynamics (14th Edition)

Ch. 16.3 - When the gear rotates 20 revolutions, it achieves...Ch. 16.3 - The flywheel rotates with an angular velocity of ...Ch. 16.3 - The flywheel rotates with an angular velocity of (...Ch. 16.3 - The bucket is hoisted by the rope that wraps...Ch. 16.3 - A wheel has an angular acceleration of = (0.5 )...Ch. 16.3 - For a short period of time, the motor turns gear A...Ch. 16.3 - Prob. 1P Ch. 16.3 - The angular acceleration of the disk is defined by...Ch. 16.3 - The disk is originally rotating at 0 = 12 rad/s....Ch. 16.3 - Prob. 4P

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The velocity and acceleration of the ball at the instant.

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