Law of circular motion

[yellowshark]

Need your help on this one guys. If an object is moving in a circle with a constant radius and constant speed why is it constantly accelerating?

Yup we are still revising and not racing

[mattsedgley]

"Circular motion is accelerated even if the angular rate of rotation is constant, because the object's velocity vector is constantly changing direction. Such change in direction of velocity involves acceleration of the moving object by a centripetal force, which pulls the moving object towards the center of the circular orbit. Without this acceleration, the object would move in a straight line, according to Newton's laws of motion."

[yellowshark]

Thanks Matt; I should have course guessed that you would know! Can we go a bit deeper please.

1. So the Centripal force which keeps it in a circular motion, else it would go straight.
2. At the same time this force is accelerating the object.
3. Why does the speed not get faster?
4. Why does the object retain the same radius rather than move inexorably to the centre?


And, if the scenario is actually a ball on the end of a length of string - does the same concept apply? IE I would have thought it was the string that was preventing the object going in a straight line.

[mattsedgley]

mate - not gonna lie - i copied that box from wikipedia! - however if you really want me too... we've got a physics Dr at school I'll print the thread and ask your questions for you.

I covered this about 6 years ago, so i'm more than rusty!

[wessex88]

Just like a ball on a piece of string.The string aplies the centriptal force preventing the ball continuing in a straight line.The ball is accelerating towards the centre continually otherwise it would continue in astraight line flying off at a tangent.The speed does not vary because the radius is constant.Shorten the string whilst spinning and the speed would increase,lengthen and the speed reduces.Just watch an ice skater doing spins,the arms are drawn in to increase the speed of rotation.The object retains the same radius as the centipetal force pulling the object towards the center is equal to the centrifugal force trying to pull the object further away from the center.

[yellowshark]

Thanks guys. About time to move this to the RC arena and make it useful. Just before I do that, I am getting the gist, but I think it demonstrates the difference between the academic World and life in general. Normal people like me equate accelerating to increasing speed. If I am going along and start to turn, as I am changing direction then I am changing velocity and therefore accelerating. The reality is though that I will slowing down!

Now for interesting stuff. Doing some reading, one of the forces that provides the centripetal force is friction eg a TC going around a bend. Now a heavier object requires more centripetal force, in this case friction. So a 1350 TC will need less friction that a 1500 TC. So does that mean
a) A 1350 TC will corner better because it needs less friction
b) Or a 1500 will because the extra weight increases friction?

[issac]

you need to put awarning before reading this type of thread

"take 2 asprins and a stiff drink before reading below"

[Reuben]

Ide say the best way to find A or B would be to get to the track and try it out!!



Where you and Craig been Pete? 13.5 is looking rather quiet, I might even have to go back to 17.5 for next champ

[Reuben]

Plus ide guess that its more than just weight and centripetal forces that effect the cornering - as a lighter car will require less force = less tyre wear.

But as to what corners better, I think it depends on how the rubber compound is effected (and how it grips) depending on much much static and dynamic weight is applied.

[yellowshark]

May 30, 2010 18:10:05 GMT Reuben said:

Where you and Craig been Pete? 13.5 is looking rather quiet, I might even have to go back to 17.5 for next champ

Afraid you can't race TC and become a nuclear phycisist Reuben.
I think it is still another 4 weeks before we will hit the track again; I know we will have just 4 weekends - assuming it doesn't rain - to get car, esc, rusty driver and mechanic up to speed for the Juniors, let alone the Aldershot Nats the week before.

The good news is it has finally given me the time to debug and fix an obscure electrical fault which has kept my yellow Corvette in the garage these past 2 years ;D

[yellowshark]

Problem solved! Its amazing that when some things are so obvious you just don't see them. Hanging out on the XRAY forum this popped up.




I thought about doing a test like this before, but never found the time...

Here is my thoughts:

If you run a circle as fast as you can, there are two forces that are balanced: centripetal force and friction force of the tires.

As you mentioned centripetal force ist proportional to mass.

If tire friction was dry friction, you would have the maximum possible friction force also proportional to mass:
Ff=µ*Fn with µ=coefficient of friction and Fn=weight=m*g and g=gravitational acceleration (9.81 m/s²).

If you are at maximum cornerspeed you can set them equal:

Ff=CF
µ*m*g=m*v²/r

as you see mass is on both sides of the eqation and you can calculate cornerspeed:

v²=µ*g*r or v=squareroot(µ*g*r)

However µ is not constant for tyres, and depends from weight, speed, camber, slip angle, temperature and other parameters, so there will be an influence of weight on cornerspeed.

Another aspect is aerodynamic forces: if you have some aerodynamic downforce, this will increas cornerspeed because it raises the friction force without adding weight, so your centripetal force stays constant. This effect is bigger, if the car has less mass.