Explanation Given: The equation of radial coordinate , Peg P fork link O A is shown in Figure (1). The radial coordinate ( r ) is e θ . The angular velocity ( θ ˙ ) is 2 rad/s . The angular acceleration ( θ ¨ ) is 4 rad/s 2 . The angular position ( θ ) is π 4 rad . Write the expression for the radial coordinate ( r ) . r = e θ (I). Here, angular position is θ . Write the expression for the radial acceleration. a r = r ¨ − r θ ˙ 2 (II). 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 ˙ (III). 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 (IV). The magnitude of the acceleration is a , radial acceleration is a r and transverse acceleration a θ . Differentiate Equation (I). r = e θ r ˙ = e θ θ ˙ (V). Differentiate Equation (V). r ˙ = e θ θ ˙ r ¨ = e θ θ ¨ + e θ θ ˙ 2 (VI). Conclusion: Substitute π 4 for θ in Equation (I). r = e θ r = e ( π 4 ) m =2 .1933 m Substitute π 4 for θ and 2 rad/s for θ ˙ in Equation (V)

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Chapter 12, Problem 36FP

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The radial and transverse components of the peg's acceleration.

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The radial and transverse components of the peg's acceleration.

Solution Summary: The equation of radial coordinate, Peg P fork link OA is shown in Figure (1).

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The radial and transverse components of the peg's acceleration.

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