Vector Calculus to derive Newton's second law

[pestydestroyer]

THIS THREAD HAS BEEN MOVED FROM ANOTHER FORUM BECAUSE IT IS HOMEWORK. BUT THERE IS NO TEMPLATE.

Hi everyone,
The problem gives that a particle moves in a circle with angular velocity ω. I know that r×ω=v, which is the velocity of the particle. However, I am told to differentiate and find τ=Iα but, using the product rule, I found a=(v×ω)+(r×α). I am not sure where to go from here as these quantities don't seem familiar to me. Was there a step I missed or is there something I am missing in this step?
Thanks so much for any help.

 

[jedishrfu]

Do you see any vectors that are parallel to one another?

Also this looks like a homework problem and so you should edit your post to use the homework template otherwise someone will delete it and warn you.