Is conservation of angular momentum a hoax?

[Chozen Juan]

Homework Statement

(This is a problem I myself created, so it may sound a bit trivial/stupid.) A particle of mass m in the xy plane has velocity v and a radius vector r with respect to some origin. After some time Δt, the same particle has velocity v and a radius vector r' with respect to the origin. Throughout the particle's motion, the (supposedly) isolated system consisting of this particle is not subject to any external force nor any external torque.

m(r x v) ≠ m(r' x v)
L_i ≠ L_f

Clearly, angular momentum of the system about the origin is not conserved even though there is no net external torque on the system.

Is the following statement false? "If the net external torque acting on a system is zero, the angular momentum L of the system remains constant, no matter what changes take place within the system."

Attached is a figure of the problem.

Homework Equations

L [/B]= m(r x v)

The Attempt at a Solution

I'm stumped!

 

[conscience]

m(r x v) ≠ m(r' x v)

Why do you think the two expressions are not equal ?

Do you know how to calculate cross product of two vectors ? If not , please look up and your confusion will be resolved .

 

[Chozen Juan]

Why do you think the two expressions are not equal ?

Do you know how to calculate cross product of two vectors ? If not , please look up and your confusion will be resolved .

SHOOT! I knew there was something stupid about this problem. I thought they weren't equal since the angles between the position and velocity vectors were different... but like an idiot, I forgot to take into account that the position vector changes magnitude as well. I have no idea how I missed that. This didn't even have to do with physics. It was purely a math problem.