Explanation Given: The polar coordinate ( r ) of the particle is e a t . The transverse coordinate of the particle ( θ ) is t . Write the expression for the polar coordinate ( r ) . r = e a t (I). Write the expression for the transverse coordinate ( θ ) . θ = t (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 transverse 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 transverse 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 ˙ . Differentiate Equation (I). r = e a t r ˙ = a e a t (VII). Differentiate Equation (VII). r ˙ = a e a t r ¨ = a 2 e a t Differentiate Equation (II). θ = t θ ˙ = 1 (VIII). Differentiate Equation (VIII). θ ˙ = 1 θ ¨ = 0 Conclusion: The path for r = f ( θ ) is shown in Figure (1). Thus, the path for r = f ( θ ) is shown in Figure (1)

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Author: HIBBELER

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Chapter 12, Problem 162P

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The radial and transverse components of velocity and acceleration of the particle.

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Chapter 12, Problem 161P

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The radial and transverse components of velocity and acceleration of the particle.

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