Explanation Given: The polar coordinate, peg P and angular velocity is shown in Figure (1). The angular velocity ( θ ˙ ) is 3 rad/s . The radial coordinate ( r ) is 0.5 m . The transverse coordinate ( θ ) is π 3 rad . From the figure write the expression for the radial coordinate ( r ) . r = 0.4 θ m (I). Write the expression radial velocity. υ r = r ˙ (II). Here, radial velocity is υ r and radius of the particle is r . Write the expression transverse velocity. υ θ = r θ ˙ (III). Here, transverse velocity is υ θ , radius of the particle is r and angular velocity is θ ˙ . Write the expression for the radial acceleration. a r = r ¨ − r θ ˙ 2 (IV). Here, radial acceleration is a r and second time derivative of radius ( r ) is r ¨ . Write the expression for the transverse acceleration. a θ = r θ ¨ + 2 r ˙ θ ˙ (V). Here, transverse acceleration is a θ and second time derivative of θ is θ ¨ and first time derivative of radius ( r ) is r ˙ . Differentiate Equation (I). r = 0.4 θ m r ˙ = 0.4 θ ˙ m (VI). Differentiate Equation (VI). r ˙ = 0.4 θ ˙ m r ¨ = 0.4 θ ¨ m (VII). Write the expression for the angular velocity ( θ ˙ ) . θ ˙ = 3 rad/s (VIII). Differentiate Equation (VIII). θ ˙ = 3 rad/s θ ¨ = 0 Conclusion: Substitute 0.5 m for r in Equation (I). r = 0.4 θ m ( 0.5 m ) = 0.4 m θ θ = 1.25 rad Substitute 3 rad/s for θ ˙ in Equation (VI). r ˙ = 0.4 θ ˙ m = 0

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 12.8, Problem 169P

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The velocity and acceleration of the particle:

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Chapter 12.8, Problem 168P

Chapter 12.8, Problem 170P

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Engineering Mechanics: Statics & Dynamics (14th Edition)

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The velocity and acceleration of the particle:

Solution Summary: The polar coordinate, peg P and angular velocity are shown in Figure (1).

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The velocity and acceleration of the particle:

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