# What is the speed of each particle relative to the other?

• pivoxa15
The method you suggested in #3 is only applicable for events in the same frame, not for transforming velocities from one frame to another.In summary, two particles are shot out simultaneously from a given point with velocity v and start at right angles to each other. The relative velocity of one particle to the other can be calculated by subtracting the velocity vectors, resulting in a speed of v√2. However, for relativistic speeds and non-parallel velocities, the vector form of the relativistic velocity addition formula must be used. This formula is also necessary for transforming velocities from one frame to another.
pivoxa15
Two particles are shot out simultaneously from a given point with velocity v. They start at right angles to each other. What is the speed of each particle relative to the other?

I got one particle thinks the other one is traveling at $$v\sqrt2$$ whereas they are traveling at v and vice versa. But I think I calculated it from a frame that is at rest relative to both particles and imagined what each particle would think if they had information in my frame.

Last edited:
pivoxa15 said:
Two particles are shot out simultaneously from a given point with velocity v. They start at right angles to each other. What is the speed of each particle relative to the other?

I got one particle thinks the other one is traveling at $$v\sqrt2$$ whereas they are traveling at v and vice versa. But I think I calculated it from a frame that is at rest relative to both particles and imagined what each particle would think if they had information in my frame.
If you stick to a vector analysis, it is not so confusing. The relative velocity of a to b is the velocity of a relative to the origin - velocity of b relative to the origin (or + the velocity of the origin relative to b). So just subtract the velocity vectors.

The relative velocity, therefore is $\vec v_a + (-\vec v_b)$. Relative speed is the length of that vector, which is the hypotenuse of a right triangle with sides of length v: $v_{rel}\sqrt{2v^2} = \sqrt{2}v$.

AM

Last edited:
So veclocity of a to b is usually just $\vec v_a -\vec v_b$.

So if we look at another example, ship a is traveling at 4c/5. ship b is traveling at 3c/5 in 1D motion. The relative velocity of ship a to b or what ship b thinks a is traveling is $v_a -v_b = c/5$.

Last edited:
If the speeds are relativistic and in different directions, you need to use the vector form of the relativistic "velocity addition" formula. See the section "The velocity addition formula for non-parallel velocities" on the following page from the Usenet Physics FAQ:

http://math.ucr.edu/home/baez/physics/Relativity/SR/velocity.html

Last edited:
But if I am just doing velocity addition for different frames (not events in frame), i.e know what the other frame is traveling relative to me, do I still need the relativistic addition formula? If I do apply it than I could pretend the 'event' is a person standing still in the other frame. So the velocity of that person is 0 in their frame S'. I get the speed I see them is v the relative velocity of the frames. This value can be calculated with the method I suggested in #3?

pivoxa15 said:
But if I am just doing velocity addition for different frames (not events in frame), i.e know what the other frame is traveling relative to me, do I still need the relativistic addition formula?
Yes. The relativistic addition formula tells you how velocities transform from one frame to another, which is what you want.

## What is the concept of relative speed between particles?

The concept of relative speed between particles refers to the speed at which two particles are moving in relation to each other. It takes into account the motion of one particle with respect to the other, rather than their individual speeds.

## How is relative speed calculated between particles?

To calculate relative speed between particles, you need to subtract the speed of one particle from the speed of the other. The resulting value will be the relative speed between the two particles. This calculation can be done in any frame of reference.

## Can relative speed between particles be negative?

Yes, relative speed between particles can be negative. This indicates that the two particles are moving in opposite directions. A negative relative speed does not necessarily mean that one particle is moving backwards, as it is relative to the other particle's motion.

## Does the mass of particles affect their relative speed?

Yes, the mass of particles can affect their relative speed. Particles with a greater mass will typically have a slower relative speed compared to particles with a smaller mass, assuming their individual speeds are the same.

## Why is understanding relative speed between particles important in science?

Understanding relative speed between particles is important in science because it helps us understand the interactions between particles and how they move in relation to each other. This is crucial in fields such as physics, chemistry, and astronomy, where the behavior of particles plays a significant role in explaining natural phenomena.

Replies
3
Views
1K
Replies
4
Views
850
• Special and General Relativity
Replies
9
Views
465
Replies
7
Views
2K
Replies
3
Views
1K
Replies
6
Views
1K
Replies
2
Views
1K
• Quantum Physics
Replies
5
Views
508
• Introductory Physics Homework Help
Replies
12
Views
2K