Understanding Polar Vector Plots and Phases in Vector Algebra

In summary, the conversation is about a problem involving a vector in polar notation and the application of vectors to phases and periodicity. The solution involves analyzing the vectors in a given amount of time and finding the distance traveled along the x-axis. The textbook being referenced is "Mathematical Methods for Physics and Engineering" and there has been no mention of phasors in the chapter on vectors.
  • #1
unscientific
1,734
13

Homework Statement



The problem is attached in the picture.


The Attempt at a Solution



This looks like a vector in polar notation to me (r, θ). But the application of vectors to phases and periodicity is not even mentioned in the chapter! (Vector Algebra)

I've tried to make sense of it but I'm not sure what's going on in the solutions..

What I think is this:
given 2 vectors of equal length, one with θ = 0 and another with θ = 45o, in a given amount of time the inclined vector travels a shorter distance along x. Specifically:

x' = x cos (45)


I'm not sure if I'm correct to analyse it in this way..
 

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  • #2
unscientific said:

Homework Statement



The problem is attached in the picture.

The Attempt at a Solution



This looks like a vector in polar notation to me (r, θ). But the application of vectors to phases and periodicity is not even mentioned in the chapter! (Vector Algebra)

I've tried to make sense of it but I'm not sure what's going on in the solutions..

What I think is this:
given 2 vectors of equal length, one with θ = 0 and another with θ = 45o, in a given amount of time the inclined vector travels a shorter distance along x. Specifically:

x' = x cos (45°)

I'm not sure if I'm correct to analyse it in this way..
What course is this for?

Has the textbook done anything with Phasors to analyze Alternating Current circuits?
 
  • #3
SammyS said:
What course is this for?

Has the textbook done anything with Phasors to analyze Alternating Current circuits?

This is from chapter 7, Vector Algebra of "Mathematical Methods for Physics and Engineering" by Riley, Hobson and Bence.

Nope, this is the first chapter on vectors.
 

1. What is a polar vector plot and how is it used in science?

A polar vector plot is a graphical representation of a vector quantity, such as force or velocity, in a polar coordinate system. It is often used in science to visualize and analyze the direction and magnitude of a vector in relation to a specific origin point.

2. How are the phases of polar vector plots determined?

The phases of polar vector plots are determined by the angle of the vector with respect to the horizontal axis, typically measured in degrees or radians. The starting point of the vector is also taken into consideration when determining the phase.

3. What are the main differences between polar vector plots and Cartesian vector plots?

The main difference between polar vector plots and Cartesian vector plots is the coordinate system used. Polar plots use a polar coordinate system, with angles and radii, while Cartesian plots use a Cartesian coordinate system, with x and y coordinates. Additionally, polar plots are better for visualizing circular or rotational motion, while Cartesian plots are better for linear motion.

4. How can polar vector plots be used to analyze the motion of an object?

Polar vector plots can be used to analyze the motion of an object by showing the changing direction and magnitude of the object's velocity or acceleration over time. By analyzing the phases and lengths of the vectors, scientists can determine the speed, direction, and patterns of an object's motion.

5. Can polar vector plots be used in fields other than physics?

Yes, polar vector plots can be used in various fields, such as engineering, meteorology, and even biology. In engineering, they can be used to analyze forces and moments in structures. In meteorology, they can be used to analyze wind patterns. In biology, they can be used to analyze the direction and speed of animal movement.

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