Rotation!............plz help?

Question

a meter stick is held vertically with one end on the floor and is then allowed to fall. Find the speed of the other end when it hits the floor, assuming that the end on the floor doesn't slip.

Answer 1

When the stick hits the floor it has lost gravitational potential energy = 0.5mg.

total kinetic energy = lateral kinetic energy + rotational kinetic energy

lateral kinetic energy = 1/2m(V/2)^2 at the center of mass.

rotational kinetic energy = 1/2I(V/r)^2. r=1, I = (1/3)ml^2, l=1

(1/2)I(V/r)^2 = (1/2)(1/3)mV^2

total kinetic energy = (1/8)mV^2 + (1/6)mV^2 = (7/24)mV^2

(7/24)mV^2 = 0.5mg

(7/24)V^2 = 0.5g

V^2 = (12/7)g

V = sqrt{(12/7)g}

V = 4.09878

V = 4.1 m/s

Answer 2

i would think is 9.8mph cus all gravity pulls down at a same speed without air resistance. I"m not sure, but i think i'm close