# Decomposing velocity vectors into polar axis

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In summary, the conversation discusses the decomposition of velocity in relation to a radar. The speaker mentions drawing the polar and standard axis centered in the particle and identifying angles equal to 60° to decompose the velocity. They also mention the confusion surrounding the velocity "cutting" the angle and the need to draw the angular component at a right angle from the head of the radial component. Additionally, the conversation mentions that the angular component is perpendicular to the radial component and the vector sum of these components is the velocity vector. The speaker suggests using a picture to better understand the concept.
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Homework Statement
A particle moves along a trajectory with velocity whose modulus is constant. At a certain time it is at a point of the trajectory whose radius of curvature is 15 m. At this moment, the modulus of the acceleration is 10 m/s^2. A radar detects that the particle, located 40 m above the ground, moves towards it with velocity v=5 m/s. The radius vector that goes from the radar to the particle forms an angle of 60° with the ground.
Find the angle formed by the velocity and the angular coordinate.
Relevant Equations
v=(dot r; r dot theta) in polar coordinates
Well, I drew the polar and standard axis centered in the particle and wrote which angles were equal to 60° so I could decompose the velocity. The problem says "moves towards it (the radar) with velocity v=5 m/s, so that's one of the components. But I realized that the velocity "cuts" the angle, so I don't know how I should decompose the velocity. Maybe it's a silly question, but it confuses me.

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• 20190831_163323.jpg
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The angular component is perpendicular to the radial component, so draw it at a right angle from the head of the radial component toward the velocity vector.

tnich said:
The angular component is perpendicular to the radial component, so draw it at a right angle from the head of the radial component toward the velocity vector.

So the velocity would have the same direction that the angular component?

tnich
No, that would just be the way to draw than angular component. The angular velocity component is perpendicular to the radial component (radial with respect to the radar's positions). Their vector sum is the velocity vector.

Last edited:
tnich said:
No, that would just be the way to draw than angular component. The angular velocity component is perpendicular to the radial component (radial with respect to the radar's positions). Their vector sum is the velocity vector.
It looks like you are stuck on this part. You need to decompose the velocity vector into two perpendicular components, one pointing toward the radar. Maybe a picture would help.

## 1. What is the concept of decomposing velocity vectors into polar axis?

The concept of decomposing velocity vectors into polar axis involves breaking down a two-dimensional velocity vector into its vertical and horizontal components, which are then represented by polar coordinates. This allows for a better understanding and analysis of the motion of an object.

## 2. Why is it important to decompose velocity vectors into polar axis?

Decomposing velocity vectors into polar axis is important because it helps to simplify the analysis of motion in two dimensions. It allows for a better visualization and understanding of the direction and magnitude of an object's motion, which can be useful in various fields of science and engineering.

## 3. How do you decompose a velocity vector into polar axis?

To decompose a velocity vector into polar axis, you must first determine the angle between the vector and the x-axis. This angle, along with the magnitude of the vector, can be used to calculate the vertical and horizontal components using trigonometric functions. These components can then be converted into polar coordinates.

## 4. What are some real-world applications of decomposing velocity vectors into polar axis?

Decomposing velocity vectors into polar axis has many real-world applications, such as in physics, engineering, and navigation. For example, it can be used to analyze the motion of projectiles, determine the velocity of an object in different directions, and navigate objects in two-dimensional space, such as aircraft and ships.

## 5. Are there any limitations to decomposing velocity vectors into polar axis?

While decomposing velocity vectors into polar axis is a useful tool, it does have its limitations. It assumes that the object is moving in a two-dimensional plane, which may not always be the case. It also does not take into account any external forces acting on the object, which may affect its motion. Additionally, the accuracy of the decomposition depends on the precision of the measurements and calculations used.

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