# Reference frame in collision problems

• feynman1
In summary: There is no inertial reference frame in which Ball 2 is always fixed.Yes. There is no inertial reference frame in which Ball 2 is always fixed.

#### feynman1

2 balls (Ball 1 and Ball 2) collide fully elastically and their relative velocity stays the same as but in sign opposite to that before the collision. Is there any sort of reference frame in which Ball 2 is always fixed (at rest) so that one can look at their relative velocity always in that reference frame? Here 'always' includes before and after the collision.

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feynman1 said:
Is there any sort of reference frame in which Ball 2 is always fixed (at rest) so that one can look at their relative velocity always in that reference frame?
Yes, the rest frame of Ball 2 is such a frame of reference (surprise!), but it is not inertial and therefore not necessarily a good choice to describe the process.

Dale and feynman1
DrStupid said:
Yes, the rest frame of Ball 2 is such a frame of reference (surprise!), but it is not inertial and therefore not necessarily a good choice to describe the process.
Do you mean it's not inertial at the instant of the collision but inertial before and after? If so, Ball 2 won't be fixed in that frame, which isn't what I look for.

feynman1 said:
2 balls (Ball 1 and Ball 2) collide fully elastically and their relative velocity stays the same as that before the collision. Is there any sort of reference frame in which Ball 2 is always fixed (at rest) so that one can look at their relative velocity always in that reference frame? Here 'always' includes before and after the collision.
Relative velocity is per definition the velocity of ball A in the rest frame of ball B (or vice versa). But if the relative velocity doesn't change, then there is not much of a collision.

feynman1 said:
Do you mean it's not inertial at the instant of the collision but inertial before and after? If so, Ball 2 won't be fixed in that frame, which isn't what I look for.
It is not inertial at the instant of the collision because Ball 2 (which is accelerated during the collision) is fixed in that frame.

feynman1
A.T. said:
Relative velocity is per definition the velocity of ball A in the rest frame of ball B (or vice versa). But if the relative velocity doesn't change, then there is not much of a collision.
Just edited the original question, relative v changes sign.

DrStupid said:
It is not inertial at the instant of the collision because Ball 2 (which is accelerated during the collision) is fixed in that frame.
Right, then have you an answer to the original question?

feynman1 said:
Right, then have you an answer to the original question?

Dale said:
I knew all along that such a frame written in post 2 doesn't work well. Then can we conclude that there's no inertial reference frame in which Ball 2 is always fixed?

feynman1 said:
Then can we conclude that there's no inertial reference frame in which Ball 2 is always fixed?
Yes.

## What is a reference frame in collision problems?

A reference frame in collision problems is a coordinate system used to describe the motion of objects involved in a collision. It can be either an inertial frame, where Newton's laws of motion apply, or a non-inertial frame, where additional forces must be taken into account.

## Why is it important to define a reference frame in collision problems?

Defining a reference frame is important because it allows for a consistent and accurate analysis of the collision. It helps to identify the initial and final positions, velocities, and accelerations of the objects involved, and simplifies the calculation of their interactions.

## Can the choice of reference frame affect the outcome of a collision problem?

Yes, the choice of reference frame can affect the outcome of a collision problem. In an inertial frame, the laws of physics are consistent and the outcome of the collision will be the same regardless of the reference frame chosen. However, in a non-inertial frame, additional forces may be present, leading to different outcomes.

## How do you determine the reference frame to use in a collision problem?

The choice of reference frame depends on the specific problem. In most cases, an inertial frame is preferred as it simplifies the analysis. However, if the objects involved are accelerating or rotating, a non-inertial frame may be necessary.

## Can multiple reference frames be used in a collision problem?

Yes, multiple reference frames can be used in a collision problem. This is often done to simplify the analysis or to consider different perspectives. However, it is important to ensure that all frames are consistent and do not lead to conflicting results.