Vector Calculus to derive Newton's second law

AI Thread Summary
The discussion revolves around deriving Newton's second law using vector calculus, specifically for a particle moving in a circle with angular velocity ω. The user has identified the relationship between radius and velocity (r×ω=v) but is struggling with differentiating to find torque (τ=Iα). They applied the product rule and derived a=(v×ω)+(r×α), expressing confusion over the unfamiliar quantities involved. Additionally, there is a reminder about the importance of using a homework template to avoid potential deletion of the post. Clarification on the relationships between the vectors involved is sought to progress further.
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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.
 
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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.
 
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