Calculate v - w*r: Vector, Cross Product

  • Thread starter Isawyou0
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In summary, the conversation discusses the concept of angular velocity and its relation to vector velocity in two and three dimensions. The formula for calculating relative velocity is also mentioned, with a reference to a Wikipedia article for further explanation. The idea of the cross product is also brought up in relation to the vector equation.
  • #1
Isawyou0
13
0
Hi!
seems crazy! but what if there is vx and vy?r is it a vector?
w*r can be a cross product?
 
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  • #2
It would help if you defined your symbols.
 
  • #3
Isawyou0 said:
Hi!
seems crazy! but what if there is vx and vy?r is it a vector?
w*r can be a cross product?

This wikipedia article should help: https://en.wikipedia.org/wiki/Angular_velocity

(see the part about particle motion in 3 dimensions...) :smile:
 
  • #4
yes, yes, means that v=wr gives v in one dimension, right!
I want to calculate relative velocity, v1 = v + wr - ( v' + w'r' ) ; since that v is in 2d(v for x and y in euclidean space, as a vector velocity);
 
  • #5
Isawyou0 said:
yes, yes, means that v=wr gives v in one dimension, right!
I want to calculate relative velocity, v1 = v + wr - ( v' + w'r' ) ; since that v is in 2d(v for x and y in euclidean space, as a vector velocity);

But the wikipedia page also shows the vector equation:

which, by the definition of the cross product, can be written:

115d67943a5d57b75784387fe225ccee.png
 
  • #6
isn't it like:
v=w*r.perpendicular();
 

1. What is a vector?

A vector is a mathematical quantity that has both magnitude and direction. It is commonly represented by an arrow pointing in the direction of the vector, with the length of the arrow representing the magnitude.

2. What is a cross product?

A cross product is a mathematical operation performed on two vectors that results in a new vector that is perpendicular to both of the original vectors.

3. How is the cross product calculated?

The cross product of two vectors, v and w, is calculated by taking the magnitude of v and w, multiplying them together, and then multiplying that by the sine of the angle between the two vectors. This can also be represented as v x w = |v| * |w| * sin(theta).

4. What is the difference between a cross product and a dot product?

The dot product of two vectors results in a scalar value, while the cross product results in a vector. Additionally, the dot product is commutative (a * b = b * a), while the cross product is not (a x b = -b x a).

5. In what situations is the cross product useful?

The cross product is useful in situations where we need to find a vector that is perpendicular to two other vectors, such as in calculating torque or angular momentum in physics. It is also used in 3D computer graphics and animation to determine the orientation of objects in space.

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