Explanation Given: The radial distance ( r ) is 2 m . The angular position ( θ ) is 5 t 2 rad . The final angle displacement is θ = 30 ° Write the expression for the radial distance ( r ) . r = 2 θ ft (I). Here, radial distance is ( r ) . Write the expression for angular position. θ = 5 t 2 rad (II). Write the expression for the radial acceleration. a r = r ¨ − r θ ˙ 2 (III). 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 ˙ (IV). 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 acceleration. a = a r 2 + a θ 2 (V). Here, the magnitude of the acceleration is a , radial acceleration is a r and transverse acceleration a θ . Write the expression for the final angle displacement. θ = 30 ° = 30 ( π 180 ) = 0.524 rad Differentiate Equation (I). r = 2 m r ˙ = 0 (VI). Differentiate Equation (VI). r ˙ = 0 r ¨ = 0 Differentiate Equation (II). θ = 5 t 2 rad θ ˙ = 10 t rad/s (VII). Differentiate Equation (VII). θ ˙ = 10 t rad/s θ ¨ = 10 rad/s 2 Conclusion: Substitute 0

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Author: HIBBELER

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Chapter 12, Problem 9RP

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The magnitude of the particle’s acceleration when θ=30° .

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The magnitude of the particle’s acceleration when θ = 30 ° .

Solution Summary: The author explains the magnitude of the particle's acceleration when theta =30° and the expression for the radial distance.

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