Deriving dA/dt = \omega x A: Proof for Constant Vector A and Vector \omega

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In summary, the conversation discusses how to prove the derivative of a constant vector A can be written as dA/dt = ω x A, where ω is a vector and "x" is the cross product. It is suggested to differentiate the magnitude squared of A, which is also constant, to find the derivative.
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nna
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I hope somebody can help me.. this is the problem i have to proof that if A is a constant vector then I can write its derivate as dA/dt = \omega x A.. where \omega is a vector, and the "x" is the cross product
 
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  • #2
Welcome to PF!

Hi nna! Welcome to PF! :smile:

(have an omega: ω :wink:)
nna said:
I hope somebody can help me.. this is the problem i have to proof that if A is a constant vector then I can write its derivate as dA/dt = \omega x A.. where \omega is a vector, and the "x" is the cross product

(You mean "if A is constant in magnitude".)

Hint: if the magnitude is constant, then so is the magnitude squared, which is A.A. :wink:
 
  • #3
Sorry :( but I don't understand how that helps...
 
  • #4
Differentiate it …

what do you get? :smile:​
 
  • #5
ok ok thank you so much! it really helps... jaja it was very easy sorry
 

1. What does the equation dA/dt = \omega x A represent?

The equation dA/dt = \omega x A represents the change in the magnitude of vector A over time, where \omega is the angular velocity and x represents the cross product.

2. How is the proof for constant vector A and vector \omega derived?

The proof for constant vector A and vector \omega is derived using the properties of cross products and the definition of angular velocity. It involves manipulating the equation to show that the derivative of the magnitude of vector A over time is equal to the cross product of \omega and A.

3. Why is it important to prove this equation?

Proving this equation is important because it helps us understand the relationship between angular velocity and the change in magnitude of a vector. It also allows us to use this equation in various applications, such as kinematics and dynamics.

4. Can this equation be applied to non-constant vectors?

No, this equation only applies to constant vectors. If the magnitude of vector A is changing over time, then the proof for this equation would not hold.

5. How is this equation used in physics and engineering?

This equation is used in physics and engineering to describe the motion of rotating objects and systems. It is also used in calculations involving angular momentum and torque. Additionally, it can be used to understand and predict the behavior of rotating bodies, such as gyroscopes.

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