Explanation Given: The angular velocity ( θ ˙ ) is 4 rad/s . The transverse coordinate ( θ ) is π 2 rad . Write the expression for the polar coordinate ( r ) . r = 8 θ ft (I). Write the expression radial velocity. υ r = r ˙ (II). Here, radial velocity is υ r and radius of the particle 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 = 8 θ ft r ˙ = 8 θ ˙ ft (VI). Differentiate Equation (VII). r ˙ = 8 θ ˙ ft r ¨ = 8 θ ¨ ft (VII). Differentiate Equation (II). θ ˙ = 4 rad/s θ ¨ = 0 (VIII). Substitute π 2 rad for θ ˙ in Equation (I). r = 8 θ ft = 8 ( π 2 ) ft = 4 π ft Substitute 4 rad/s for θ ˙ in Equation (VI). r ˙ = 8 θ ˙ ft = 8 ( 4 ) ft/ s =32 ft/ s Substitute 0 for θ ¨ in Equation (VII)

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Chapter 12, Problem 189P

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The velocity and acceleration of the particle when θ is π2 and sketch the components on the curve.

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Chapter 12, Problem 188P

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The velocity and acceleration of the particle when θ is π 2 and sketch the components on the curve.

Solution Summary: The velocity and acceleration components on the curve are shown in Figure (1).

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The velocity and acceleration of the particle when θ is π2 and sketch the components on the curve.

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