# Central force w1/w2=√r2/r1

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Hi
we are going through cirkular centralforce and Im complete stuck...
I cant find the derivation to why w1/w2=√r2/r1 is correct

w1/w2=√r2/r1

sorry im lost...
best regards
Fred

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Dick
Homework Helper
Hi
we are going through cirkular centralforce and Im complete stuck...
I cant find the derivation to why w1/w2=√r2/r1 is correct

w1/w2=√r2/r1

sorry im lost...
best regards
Fred
Maybe you could explain what those symbols mean?

yes of course , sorry
There are two objects that are spinning on a plate and they fall off, and the physical reasoning is that the angular velocity (ω) has to meet the condition
ω1/ω2=√r2/r1

ω1= angular velocity objekt 1
ω2= angular velocity objekt 2
r2= objet 2 position to the center of the plate
r1= objet 1 position to the center of the plate

Best regards

Dick
Homework Helper
yes of course , sorry
There are two objects that are spinning on a plate and they fall off, and the physical reasoning is that the angular velocity (ω) has to meet the condition
ω1/ω2=√r2/r1

ω1= angular velocity objekt 1
ω2= angular velocity objekt 2
r2= objet 2 position to the center of the plate
r1= objet 1 position to the center of the plate

Best regards
You should probably the objects will fall of when the acceleration exceeds that which can be produced by the frictional force holding them on. Do you know that the acceleration is given by the expression ##v^2/r## where ##r## is distance from the center and ##v## is rotational speed? What's the relation between ##v## and angular velocity?

I Think that the relation is V=ωr correct? (and the friktionskoefficient is the same for both the objects)

BvU
Homework Helper
2019 Award
That is correct. Now we need an equation to express 'staying on the plate' versus 'flying off' a bit more in physics terms using the variables in our exercise.
The template had an item for that; unfortunately it has disappeared (how ?, strange !). So here is a copy:

## Homework Statement

There are two objects that are spinning on a plate and they fall off, and the physical reasoning is that the angular velocity (ω) has to meet the condition
ω1/ω2=√r2/r1

ω1= angular velocity objekt 1
ω2= angular velocity objekt 2
r2= objet 2 position to the center of the plate
r1= objet 1 position to the center of the plate

ω1/ω2=√r2/r1
V=ωr

## The Attempt at a Solution

√r2/r1 * ω1/ω2=0

√((ω1r2)/(ω2r1))=0

hmm this doenst feel right..

Dick
Homework Helper

## Homework Statement

There are two objects that are spinning on a plate and they fall off, and the physical reasoning is that the angular velocity (ω) has to meet the condition
ω1/ω2=√r2/r1

ω1= angular velocity objekt 1
ω2= angular velocity objekt 2
r2= objet 2 position to the center of the plate
r1= objet 1 position to the center of the plate

ω1/ω2=√r2/r1
V=ωr

## The Attempt at a Solution

√r2/r1 * ω1/ω2=0

√((ω1r2)/(ω2r1))=0

hmm this doenst feel right..
You haven't really done anything except for make an algebra mistake. Start from the physics. What condition will make an object fall off the plate?

BvU
Homework Helper
2019 Award

## Homework Statement

[/B]
Object 1 lies on a spinning plate at a distance ##r_1## from the axis. It flies off at angular speed ##\omega_1## (at lower speeed it is held in orbit by friction)
Object 2 lies on the same plate at a distance ##r_2## from the axis. It flies off at angular speed ##\omega_2##.
Friction coefficients are the same for both objects.
Masses of objects may or may not be the same.

Show that ##\omega_1/\omega_2=\sqrt{r_2/r_1}##

## Homework Equations

Friction force required to stay in circular orbit F = ...
Maximum centripetal acceleration friction force can provide aat fly-off speed =

...

## Homework Equations

Friction force required to stay in circular orbit F = m·v2/r
Maximum centripetal acceleration friction force can provide a at fly-off speed ac =v2/r

on the right track?

Dick
Homework Helper

## Homework Equations

Friction force required to stay in circular orbit F = m·v2/r
Maximum centripetal acceleration friction force can provide a at fly-off speed ac =v2/r

on the right track?
Right track. Now replace the ##v## with an expression involving angular velocity.

## The Attempt at a Solution

F = m·v2/r = (m* (ωr)2)/r
ac =v2/r =(ωr)2/r

Dick
Homework Helper

## The Attempt at a Solution

F = m·v2/r = (m* (ωr)2)/r
ac =v2/r =(ωr)2/r
Ok, now simplify that expression. ##a_c## doesn't depend on the mass, agree? So for any two objects ##a_c## is the same.

agree
(ωr)2/r = 2ω3r2

Dick
Homework Helper
agree
(ωr)2/r = 2ω3r2
I don't recognize the algebra you did you get that. Can you explain?

Ohh sorry calculation fault
I dont know the name in English (kvadreringsregler) (a+b)2 = a2+2ab+b2

this one is wrong! se next one..

Last edited:
or the potens rule axbx=(ab)x

## The Attempt at a Solution

I am overseeing the weight i F.
ω²r=ω²r
ω²/ω²=r/r
ω/ω=√r/r

am I right ??
[/B]

Dick
Homework Helper

## The Attempt at a Solution

I am overseeing the weight i F.
ω²r=ω²r
ω²/ω²=r/r
ω/ω=√r/r

am I right ??[/B]
Right idea. It would look much better if you'd distinguish the two values of ##\omega## and ##r##. Start from ##\omega_1^2 r_1 = \omega_2^2 r_2##.

## The Attempt at a Solution

ω21r122r2
ω2122=r2/r1
2122)=(r2/r1)
ω12=(r2/r1)

I Think i got it right ?!

Dick
Homework Helper

## The Attempt at a Solution

ω21r122r2
ω2122=r2/r1
2122)=(r2/r1)
ω12=(r2/r1)

I Think i got it right ?!
Yes, you've got it!

• SwedishFred
Thanks alot sir!
we will meet again ;-)
best regards
Fredrik