Explanation Given: The velocity ( υ ) is 20 m/s . The radial coordinate ( r ) is 60 m . Write the expression for the radial coordinate ( r ) . r = 60 m (I). Write the expression for the velocity ( υ ) . υ = 20 m/s (II). Write the expression radial velocity. υ r = r ˙ (III). Here, radial velocity is υ r and first time derivative of radius ( r ) is r ˙ . Write the expression tangential velocity. υ θ = r θ ˙ (IV). 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 (V). Here, radial acceleration is a r and second time derivative of radius ( r ) is r ¨ . Write the expression for the tangential acceleration. a θ = r θ ¨ + 2 r ˙ θ ˙ (VI). Here, transverse acceleration is a θ and second time derivative of θ is θ ¨ and first time derivative of radius ( r ) is r ˙ . Write the expression for the magnitude of the velocity. υ = υ r 2 + υ θ 2 (VII). Here, the magnitude of the acceleration is υ , radial velocity is υ r and the transverse velocity is υ θ . Write the expression for the magnitude of the acceleration. a = a r 2 + a θ 2 (VIII). The magnitude of the acceleration is a , radial acceleration is a r and transverse acceleration a θ . Write the expression to calculate the angular rate. υ = r θ ˙ (IX). Differentiate Equation (I). r = 60 m r ˙ = 0 Differentiate Equation (IX). r ˙ = 0 r ¨ = 0 Differentiate Equation (II). υ = 20 m/s υ ˙ = 0 Differentiate Equation (IX). υ = r θ ˙ υ ˙ = r ˙ θ ˙ + r θ ¨ (X). Conclusion: Substitute 0 for r ˙ in Equation (III). υ r = r ˙ = 0 Substitute 60 m for r in Equation (IV). υ θ = r θ ˙ = 60 θ ˙ Substitute 0 for υ r , 20 m/s for υ , and 60 θ ˙ for υ θ in Equation (VII)

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 12.8, Problem 183P

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The angular rate of rotation θ˙ of the radial line r and the magnitude of the truck’s acceleration a .

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Chapter 12.8, Problem 182P

Chapter 12.8, Problem 184P

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Chapter 12 Solutions

Engineering Mechanics: Statics & Dynamics (14th Edition)

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The angular rate of rotation θ ˙ of the radial line r and the magnitude of the truck’s acceleration a .

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The angular rate of rotation θ˙ of the radial line r and the magnitude of the truck’s acceleration a .

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Chapter 12 Solutions