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7 December, 16:35

Three joggers are running along straight lines as follows: Jogger A, with a mass of 55.2kg, is traveling along the line y=6.00m at 3.45 m/s in the positive x-direction. Jogger B, with a mass of 62.4kg, is traveling at 4.23 m/s along the line x=3.00m in the positive y-direction. Jogger C, with a mass of 72.1kg, is traveling at 4.75 m/s along the line x=-5.00m in the negative y-direction. What is the total counterclockwise angular momentum of the three joggers about the origin?

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  1. 7 December, 19:48
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    L = - 1361.591 k Kgm/s

    Explanation:

    Given

    mA = 55.2 Kg

    vA = 3.45 m/s

    rA = 6.00 m

    mB = 62.4 Kg

    vB = 4.23 m/s

    rB = 3.00 m

    mC = 72.1 Kg

    vC = 4.75 m/s

    rC = - 5.00 m

    then we apply the equation

    L = (mv x r)

    ⇒ LA = mA*vA x rA = 55.2 * (3.45 i) x (6 j) = (1142.64 k) Kgm/s

    ⇒ LB = mB*vB x rB = 62.4 * (4.23 j) x (3 i) = ( - 791.856 k) Kgm/s

    ⇒ LC = mC*vC x rC = 72.1 * ( - 4.75 j) x ( - 5 i) = ( - 1712.375 k) Kgm/s

    Finally, the total counterclockwise angular momentum of the three joggers about the origin is

    L = LA + LB + LC = (1142.64 - 791.856 - 1712.375) k Kgm/s

    L = - 1361.591 k Kgm/s
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