How Do You Solve These Classic Meter Stick Rotational Motion Problems?

[srnj222]

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, don't 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))

 

[srnj222]

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

 

[srnj222]

Again not sure but here's 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)