[Momentus (OP)]

How can you say the blue ball did not change its speed?

Yes I see your point. If this was a simple vector sum then it would be just as you describe.
It is not a simple vector sum. The collision is governed by Newton's laws.
Momentum is vm, velocity x mass. Velocity is a vector quantity of speed and direction.

To change momentum by changing speed, force is directed along the line of motion.
To change momentum by changing direction, force is directed at right angles to the line of motion.

Before the collision the ball is moving at 4 units in the x direction The force applied in the y direction changes the direction. All the force is reacted by the change in direction. The force required to change the speed of the red ball is reacted by the force required to change the direction of the blue ball. The speed of the blue ball does not change.
After the collision the blue ball is moving at the same speed, but in a different direction. That new direction is determined by the equal and opposite change in momentum of the two balls.
The red ball?s change in momentum is due to a change in speed. The blue balls change in  momentum. Is due to a change in direction.

Equal and opposite forces, equal and opposite momentum change.

[Bored chemist]

Timing is difficult, if the red ball impacts too early, it strikes the front of the blue ball. This slows the blue ball down and the red ball is deflected forward. If the red ball hits too late, on the back of the blue ball, it speeds the blue ball up and is deflected to the rear.

If you hit the blue ball centrally, it neither slows down nor speeds, up and the red ball is not deflected forwards or backwards. It stops.

And how good do you have to get the timing?

What is the difference between something that does not happen, and something that can only happen if you do something  impossible?

[Origin]

Yes I see your point.

Apparently not.

If this was a simple vector sum then it would be just as you describe.
It is not a simple vector sum. The collision is governed by Newton's laws.

It's not a vector sum?  Really?  So you prefer to say that the ball is moving in 2 directions at the same time??

In essence you say, "Here is the math that says the speed of the blue ball increases after the collision; but just ignore that".

That is a really damn odd way to try and make a point.

edited to remove an unnecessary insult.

[Momentus (OP)]

Here is the math that says the speed of the blue ball increases

I keep asking for some maths to show how you think that the collision works out.
I ask because I do not know how to show it mathematically.
That really does make it damn peculiar. Show the math that you refer to. please. it would really help me to understand why you have a problem with centripetal force.

[Momentus (OP)]

If a force is applied perpendicular to an object's velocity, it will alter the direction of motion without changing the speed.

I think that this applies to a blue ball rolling down a snooker table and struck by a red ball rolling across the table

Also, the red ball stops at the point of impact.

I cannot see how it can behave in any other way, but seek confirmation.

[paul cotter]

It's over 50years since I did this stuff and since I never had need to use it, I can't remember exactly. I think you look at the conditions at impact and take components of momentum and put mv=m1v1 for both components and solve.

[Momentus (OP)]

It's over 50years since I did this stuff and since I never had need to use it, I can't remember exactly. I think you look at the conditions at impact and take components of momentum and put mv=m1v1 for both components and solve.

Anyone? is that enough of a lead?

[Bored chemist]

If a force is applied perpendicular to an object's velocity, it will alter the direction of motion without changing the speed.

OK
Consider the earth orbiting the sun (In a circle- just  to make the maths easier..
The gravitational force is perpendicular to the movement of the earth.

Now imagine that we suddenly make the sun heavier or lighter.

What will happen to the motion of the earth?

Do you really think it will carry on along at the same speed?

[Halc]

You were asked to confine your posting to the lighter side.
OK, this was sort of a question, not much of an assertion, but if it turns into one, you're trolling.

If a force is applied perpendicular to an object's velocity, it will alter the direction of motion without changing the speed.

I think that this applies to a blue ball rolling down a snooker table and struck by a red ball rolling across the table

Quick experiment will falsify this.
I lay a toy train track running to the south, between my legs, and one car has a golf tee on it. Train moves at 0.1 meters per second south.  I straddle the track, armed with my favorite driver. When the ball comes into optimal position, I give it a tremendous westward whack, what you are calling a force perpendicular to the object's southbound velocity.  By your assertions, the ball will attain a new velocity of 0.1 m/sec mostly west and will only make it past the edge of the track because it's falling off the tee and not go 200 meters.

Back to your topic: Kindly compute the force between the two balls. If you cannot do that, then learn some physics and stop asserting nonsense.

[Momentus (OP)]

Do you really think it will carry on along at the same speed?

Please point out the difference between rpm and tangential speed. Try the skater example. Please, this is a science forum.

[alancalverd]

Snooker balls are actually complicated because they are rolling, spinning and skidding on a frictional surface, but you could consider the collision of two ideal perfectly elastic projectiles. Then simply apply conservation of energy and momentum to see what happens.

[Origin]

I keep asking for some maths to show how you think that the collision works out.

How can you possibly think you know what happens after a collision if you can't properly analyze it?
Here is how you would calculate the final speed of the blue ball based on your results.
I don't like using the term 'units' for velocity, so let's use furlongs per fortnight.  Just kidding let's use m/s.
According to you after the collision the velocity in the x direction is 4 m/s and the velocity in the y direction is 3 m/s.
The formula to find the length (speed) of the line is:  square root {x^2 + y^2}.
The final speed of the blue ball according to your analysis is: square root {x^4 + y^3} = 5 m/s.

[Momentus (OP)]

consider the collision of two ideal perfectly elastic projectiles

Yes. do that please. Give an answer. The question is what happens according to Newton's laws?
I get a lot of good advice as to what I need to do. What happens when two perfect bodies collide? If you know, share it, for the sake of whatever deity you hold dear.

[Momentus (OP)]

By your assertions, the ball will attain a new velocity of 0.1 m/sec mostly west and will only make it past the edge of the track because it's falling off the tee and not go 200 meters.

Excellent challenge. I do not have an answer. That is why I have asked the question. It could be that it is not only the mv of the club head that is involved, but your magnificent biceps changing the nature of the impact, only a guess.

[Bored chemist]

Setting aside the fact that you have got fairly simple Newtonian mechanics wrong, even if you were right, it would have nothing to do with dark energy or dark matter.

Please point out the difference between rpm and tangential speed.

They have different units.

Please answer my question.
Do you really thing that, for example, doubling the mass of the sun would not affect the orbital speed of the earth?

[Origin]

Yes. do that please. Give an answer. The question is what happens according to Newton's laws?
I get a lot of good advice as to what I need to do. What happens when two perfect bodies collide? If you know, share it, for the sake of whatever deity you hold dear.

I agree with your results and the are perfectly in line with Newtons laws. 
The blue ball is moving along the x-axis at 4 m/s and the red ball is moving along the y-axis at 3 m/s.  The collision occurs in such a way that the impact is on top of the blue ball, so the momentum transfer is in the y direction.  Assuming a instantaneous perfectly elastic collision on the y axis the momentum of the red ball would be transferred to the blue ball.  This will result in the red ball stopping and the blue ball moving in the y direction at 3 m/s.  The blue ball will continue to move in the x direction at 4 m/s.  The resultant speed of the blue ball will be 5 m/s.

[paul cotter]

Very good,Origin. However you left out the Q.E.D. at the end!

[Momentus (OP)]

  The blue ball will continue to move in the x direction at 4 m/s.

Isaac NEWTON: Philosophiae Naturalis Principia Mathematica. 3rd Ed.
Book I Section II.
Translated and Annotated by Ian Bruce. Page 95
SECTION II. On the finding of centripetal forces.
PROPOSITION I. THEOREM I.

Truly, when the body comes to B, by a single but large impulse the centripetal force acts, and brings about that the body deflects from the line Bc and goes along in the line BC ; cC is acting parallel to BS itself, crossing BC in C; and with the second part of the time completed, the body (by the corollary to Law I.) may be found at C


Newton Centripetal.png (25.16 kB . 221x219 - viewed 133 times)

If you apply the same iterations to my original diagram you obtain the same result as shown in Newton's drawing. the blue ball maintains its original speed.
An impulse changes the direction, it does not change the speed, not in Newton's derivation of centripetal force nor in my simple diagram.

[Momentus (OP)]

doubling the mass of the sun would not affect the orbital speed of the earth?

Newton Centripetal 2.png (4.41 kB . 154x78 - viewed 104 times)

Double F, halve r  Tangential velocity remains constant. If you mean that orbital speed is the time for one orbit, then yes the revs would speed up.

[Origin]

If you apply the same iterations to my original diagram you obtain the same result as shown in Newton's drawing. the blue ball maintains its original speed.

Only the x component of the speed is constant.

An impulse changes the direction, it does not change the speed, not in Newton's derivation of centripetal force nor in my simple diagram.

Wrong.  Your diagram shows that after the collision the blue ball acquires an additional velocity of 3 m/s in the y direction.  This results in the blue ball increasing it's overall speed to 5 m/s at an angle of 36.9 degrees from the x axis.
This is all in line with Newtonian laws.
 
So once again I will point out that you got the right answer but for some reason you refuse to accept your own answer!  Your attitude is really strange.

Maybe an example will help understand.
If I drive my car in a straight line for 1 hour and I were to tell you that I ended up being 30 miles north and 40 miles west of my starting point how far away from my starting point would I be?  I would be 50 miles from my starting position.  IOW my y speed would be 30 mph and my x speed would be 40 mph and the speed along my line of travel would be 50 mph.  Hope that helps.