L = length of the meter stick = 1 m
h = height of center of mass of stick from bottom end on the floor = L/2 = 1/2 = 0.5 m
m = mass of the meter stick
I = moment of inertia of the meter stick about the bottom end
w = angular velocity as it hits the floor
moment of inertia of the meter stick about the bottom end is given as
I = m L²/3
using conservation of energy
rotational kinetic energy of meter stick as it hits the floor = potential energy when it is vertical
(0.5) I w² = m g h
(0.5) (m L²/3) w² = m g h
( L²) w² = 6g h
( 1²) w² = 6 (9.8) (0.5)
w = 5.4 rad/s
