Explanation Given: The radius ( r ) of the circular curve is 400 ft The angular velocity θ ˙ is 0.025 rad/s . The angular acceleration θ ¨ is − 0.008 rad/s 2 . Write the expression for the polar coordinate ( r ) . r = 400 ft (I). Write the expression for the angular velocity. θ ˙ = 0.025 Here, angular velocity is θ ˙ . Write the expression for the angular acceleration. θ ¨ = − 0.008 rad/s 2 Here, angular acceleration is θ ¨ . Write the expression radial velocity. υ r = r ˙ (II). Here, radial velocity is υ r and first time derivative of radius ( r ) 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 = 400 ft r ˙ = 0 (VI). Differentiate Equation (VI). r ˙ = 0 r ¨ = 0 (VII). Conclusion: Substitute 0 for r ˙ in Equation (II)

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 12.8, Problem 163P

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Chapter 12.8, Problem 162P

Chapter 12.8, Problem 164P

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Chapter 12 Solutions

Engineering Mechanics: Statics & Dynamics (14th Edition)

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The radial and transverse components of car’s velocity and acceleration and draw the components on the curve.

Solution Summary: The radial and transverse components of car's velocity and acceleration and draw the components on the curve in Figure (1).

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The radial and transverse components of car’s velocity and acceleration and draw the components on the curve.

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