Vector Calculus to derive Newton's second law

In summary, the conversation is about a homework problem involving a particle moving in a circle with an angular velocity ω. The problem asks to differentiate and find τ=Iα, but the person is stuck after using the product rule and finding a=(v×ω)+(r×α). They are seeking help and someone suggests using the homework template in their post.
  • #1
pestydestroyer
7
0
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.
 
Last edited by a moderator:
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  • #2
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.
 

1. What is Vector Calculus?

Vector Calculus is a branch of mathematics that deals with vector fields, which are quantities that have both magnitude and direction. It is used to analyze and solve problems involving forces, motion, and other physical phenomena.

2. How is Vector Calculus used to derive Newton's second law?

Vector Calculus is used to express Newton's second law, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. By using vector notation to represent forces and accelerations, we can apply the principles of vector calculus to derive this law.

3. What are the key concepts in Vector Calculus that are used to derive Newton's second law?

The key concepts used in Vector Calculus to derive Newton's second law are vector addition and subtraction, dot and cross products, and differentiation and integration of vector functions. These concepts allow us to express and manipulate forces and accelerations in a way that is consistent with Newton's second law.

4. Can Vector Calculus be used to solve other physics problems besides deriving Newton's second law?

Yes, Vector Calculus is a powerful tool that is used extensively in many areas of physics, including electromagnetism, fluid mechanics, and quantum mechanics. It is also used in engineering and computer graphics, among other fields.

5. Is knowledge of Vector Calculus necessary to understand Newton's second law?

No, while a thorough understanding of Vector Calculus can enhance our understanding of Newton's second law and its applications, it is not necessary to understand the fundamental principle. Newton's second law can be expressed and understood using basic algebra and trigonometry.

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