Finding the Radial Velocity Component of a Point P with Given Velocity Vector v

In summary, the conversation is about determining the radial component of a point's velocity. The formula for this is v_r=vcos(\theta-\alpha) where \theta,\alpha are the angle between the x direction and the radial direction and atan(vx/vy). LateX is mentioned as a tool for writing mathematical equations.
  • #1
matteo86bo
60
0
Hi there,
I'm really ashamed of doing this stupid question but I really need help with this thing. And, even if it's simple, it's not homework.

I have a point P=(x,y,z) with velocity v=(vx,vy,vz)
how can I determine the radial component of the velocity?

My answer is that, [tex]v_r=vcos(\theta-\alpha)[/tex] where [tex]\theta,\alpha[/tex] are the angle between the x direction and the radial direction and atan(vx/vy).

Is this right?
 
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  • #2
Make the dot product between the unit vector [tex]\frac{1}{\sqrt{x^{2}+y^{2}+z^{2}}}(x,y,z)[/tex] and the velocity vector, and you have the radial component of the velocity.

Hmm..doesn't LateX work todaY?
 
Last edited:
  • #3
thanks arildno,
It was really easy! It's just that sometimes I get confused with this staff.
 

FAQ: Finding the Radial Velocity Component of a Point P with Given Velocity Vector v

What is the radial component of velocity?

The radial component of velocity is the component of an object's velocity that is directed towards or away from a fixed point, also known as the origin. It represents the change in the distance between the object and the origin over time.

How is the radial component of velocity calculated?

The radial component of velocity can be calculated using the formula vr = v cosθ, where v is the total velocity of the object and θ is the angle between the object's velocity vector and the line connecting the object to the origin.

What is the difference between radial and tangential velocity?

Radial velocity is the component of an object's velocity that is directed towards or away from the origin, while tangential velocity is the component of an object's velocity that is perpendicular to the radial component. In other words, radial velocity represents the change in distance from the origin, while tangential velocity represents the change in direction of the object's motion.

How does the radial component of velocity affect circular motion?

In circular motion, the radial component of velocity determines the object's speed and the direction of its motion. As the object moves around the center, the radial component of velocity remains constant, while the tangential component changes. This is what allows the object to maintain a constant distance from the center while still changing direction.

Can the radial component of velocity be negative?

Yes, the radial component of velocity can be negative. A negative radial velocity indicates that the object is moving away from the origin, while a positive radial velocity indicates that the object is moving towards the origin.

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