Two wheels of moment of inertia 4 rotate side by side @ of 120rev/min and 240rev/min resp. in d opp directions.If now both d wheels are coupled by means of weightless shaft so that both d wheels now rotate with the common angular speed,find d new speed of rotation..

Question

anonymous · Answer

assuming angular momentum is conserved, then we first calculate the total angular momentum from the initial conditions (L - angular momentum, I - moment of inertia, w - angular velocity: L=Iw).  after attachment both discs rotate with the same angular velocity; this because the rod attaching them forces them to rotate in unison.  because they have the same moment of inertia (I) and the same angular velocity (w), they will also have equal angular momentum.  this means they split the total in half!

one final note: angular velocity is a measurement of rotations per second.  thus, we convert the given values: w1=120/60=2 and w2=240/60=4.

$$L = Iw$$$$L = 4(2) + 4(4) = 24$$ each disc rotates with angular momentum of 12 after the attachment.  rearranging:
$$w=L/I=12/4=3$$
whatcha think?