Angular velocity irrespective of axis of rotation?

[quawa99]

How exactly can the angular velocity of a 2 dimensional laminar object be the same with respect to all axes of rotation perpendicular to its plane ?

 

[namanjain]

try to do it for a rod and i applies same for others

now for this rod ____________ (anticlockwise rotation) α angular acceleration
o

with o point on it

at x dist from o
v_x = xα

at 2x dist from o
v_2x = 2xα

at 3x dist from o
v_3x = 3xα





now relative to x dist
α_rel = α
for both points 2x and 3x

rest you must do