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Rotational Motion Questions

  1. Nov 6, 2006 #1
    I'm having trouble with these two "classic meter stick problems"

    1: A rod of length L and mass M stands vertically on a flat frictionless surface. A wad of putty of mass m and initial velocity v strikes the stick at a right angle at height 3/4 L. The collision is perfectly inelastic. Find the translational and rotational motions of the object.

    2: A meter stick stands vertically at rest on a frictionless level surface. If it falls, what angular velocity will it have when it contacts the floor?

    Heres what I've got, not sure where to go from here:

    1: Momentum Initial = mv
    Momentum final = (m+M)vf

    L = mV x r = I w

    Dont know what to do with the equations

    2: I assumed a and alpha were constant, dont know if they are:

    a = L/t^2 alpha = pi/t^2 L/a = pi/alpha

    L w=pi v

    w = pi * v / L

    mg(L/2) = 1/2 mv^2 + 1/2 I w^2 >> I = 1/12 mR^2

    gL = v^2 + 1/12L^2(pi * v/L)^2

    v = (pi/L)sqrt(gL/(1+pi/12))
     
    Last edited: Nov 6, 2006
  2. jcsd
  3. Nov 6, 2006 #2
    I think I've oslved the second one now, was off by a lot before, let me know, also, still lost on the first:

    2: mgh = 1/2 I w^2

    mg(L/2)=1/2 (1/3mL^2)w^2

    g=(1/3)Lw^2

    w^2=3g/L

    w=sqrt(3g/L)=5.422 radians/second

    v = w * r = 5.422 * 1m = 5.422 m/s
     
  4. Nov 6, 2006 #3
    Again not sure but heres some progress I made on the first:

    mv = (m+M)vf

    mv x (3L/4) = Ix

    I = 1/3 ML^2 + m (3L/4)^2

    I = (1/3 M + 9/16 m)L^2

    vf (center of mass) = mv./(m+M)

    w = (3/4 mv.)/(1/3 M + 9/16 m)
     
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