Velocity in polar coordinates (again)

In summary, the poster is asking for help understanding Equation 1.11.3 in the context of plane polar coordinates. They are struggling with the concept and would appreciate a clear explanation. Another user suggests resolving the vectors into cartesian components to better understand the equation. The original poster agrees with this approach but is still having trouble understanding the method presented in the book. They apologize for being demanding and just want to fully understand.
  • #1
tiago23
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Hey people, this question was already asked here [https://www.physicsforums.com/threads/velocity-in-plane-polar-coordinates.795749/], but I just couldn't understand the answer given, so I was wondering if some of you could help me by explaining it again. I don't really get Equation (or approximation) 1.11.3, how could the magnitude of Δer be equal (or similar) to Δθ.
 

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  • #2
The easiest way to show this is to first resolve ##e_r## and ##e_{\theta}## into components in the cartesian coordinate directions:
$$e_r=e_x\cos{\theta}+e_y\sin{\theta}$$
$$e_{\theta}=-e_x\sin{\theta}+e_y\cos{\theta}$$
Are you OK with this so far?
 
  • #3
Hey @Chestermiller sorry it took so long for me to reply, internet access here is a bit precarious. I understand the derivation of this relation first decomposing the vectors into its components, and then differentiating it with relation to time, but the approach taken in the book (and the answer to the previous question) is the one I can't wrap my mind around. Sorry if this a bit capricious or demanding, I just want to understand the approach taken. :)
 

Related to Velocity in polar coordinates (again)

What is velocity in polar coordinates?

Velocity in polar coordinates is a measure of the rate of change of position with respect to time, given in terms of a distance and an angle.

How is velocity in polar coordinates calculated?

Velocity in polar coordinates is calculated using the polar coordinate system, which uses a distance from the origin and an angle from a fixed reference direction to describe a point in space.

What is the difference between velocity in polar coordinates and Cartesian coordinates?

The main difference between velocity in polar coordinates and Cartesian coordinates is the way in which the position of an object is described. While Cartesian coordinates use x and y coordinates, polar coordinates use distance and angle.

Can velocity in polar coordinates be converted to velocity in Cartesian coordinates?

Yes, velocity in polar coordinates can be converted to velocity in Cartesian coordinates using mathematical equations that take into account the angle and distance from the origin.

How is velocity in polar coordinates used in physics and engineering?

Velocity in polar coordinates is used to describe the motion of objects in circular or curved paths, which is common in physics and engineering. It also allows for a more simplified analysis of motion in certain situations, such as in rotational motion.

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