AP Physics

At time t=0, a 2kg particle has position vector r=(5.0m)i+(-8.0m)j relative to the origin. Its velocity just then is given by v=(-5.0t^2m/s)i. For the following answers, use t for the time. A) About the origin and for t>0, what is the particle's angular momentum? B) About the origin and for t>0, what is the torque acting on the particle? C) Repeat A and B for a point with coordinates (-7.0m, -4.0m, 0.0m) instead of the origin.

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  1. Please don't post under different names.

    I will be happy to critique your thinking on this.

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    bobpursley
  2. L = R x m V
    where R is position vector from reference point origin for a and b) to mass
    V is velocity vector
    x means cross or vector product

    the x coordinate of the position vector is 5 at the start but changes with time because the thing has x velocity of -5t^2
    integral = 5-(5/3) t^3

    so for part a
    L = (5-5t^3/3) i - 8 j)x(-5 t^2 i + 0 j)

    (5-5t^3/3) -8 0
    -5t^2 0 0 = -40 t^2 k
    i j k

    for part b
    Torque = rate of change of angular momentum
    dL/dt = d/dt(40 t^2 k) = 80 t

    for part c
    Rx = 5-5t^3/3 - (-7) = 12 - 5 t^3/3
    Ry = -8 -(-4) = -4
    Rz = 0 still
    just do it again

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  3. (5-5t^3/3) -8 0
    -5t^2 0 0 = +40 t^2 k
    i j k

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