Explanation Given: The radius of the gears and angular velocity are shown in Figure (1). From Figure (1) The radius r A is 1 ft . The radius r B is 2 ft . The radius r C is 0.5 ft . Time t is 3 s . The deceleration is α = 1 rad/s 2 . The angular velocity ω A is 60 rad/s Write the equation of the angular acceleration. α A = − 1 rad/s 2 Here, angular acceleration is α A . Write the expression for the magnitude of the velocity. υ A = ω r A (I) Here, velocity is υ A , angular velocity ω and radius is r A . Write the expression for the magnitude of the velocity. υ C = ω C r C (II) Here, velocity is υ C , angular velocity ω and radius is r C . Write the expression for the angular velocity. ω A = ( ω 0 ) A + α A t (III) Here, angular velocity ω , is angular acceleration is α A and time is t . Write the expression angular velocity ω B of pulley B and ω A of pulley A . ω B r B = ω A r A (IV) Here, angular velocity of pulley B is ω B , angular velocity of pulley A is ω A , radius of pulley C is r C and radius of pulley A is r A . Write the expression angular acceleration α B of pulley B and α A of pulley A . α B r B = α A r A (V) Here, angular acceleration of pulley B is α B , angular acceleration of pulley A is α A , radius of pulley C is r C and radius of pulley A is r A . Write the expression of tangential acceleration ( a A ) = α A r A (VI) Here, tangential acceleration is ( a A ) t , angular acceleration is α A and radius is r A . Write the expression of tangential acceleration ( a C ) = α B r C (VII) Here, tangential acceleration is ( a C ) , angular acceleration is α B and radius is r C . Conclusion: Substitute − 1 rad/s 2 for α A , 60 rad/s for ω A and 3 s for t in Equation (III). ω A = ( ω 0 ) A + α A t = ( 60 ) + ( − 1 ) ( 3 ) = 57 rad/s Substitute 57 rad/s for ω A , 1 ft for r A and 2 ft for r B in Equation (IV)

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Author: HIBBELER

Publisher: PEARSON

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Chapter 16, Problem 1RP

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The velocity and deceleration of the block which is being hoisted by the hub on gear B when t=3s .

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Chapter 16, Problem 147P

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The velocity and deceleration of the block which is being hoisted by the hub on gear B when t = 3 s .

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The velocity and deceleration of the block which is being hoisted by the hub on gear B when t=3s .

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