Central force w1/w2=√r2/r1

  • #1
Member warned about posting without the template and with no effort
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
 

Answers and Replies

  • #2
Dick
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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
Maybe you could explain what those symbols mean?
 
  • #3
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
 
  • #4
Dick
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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?
 
  • #5
I Think that the relation is V=ωr correct? (and the friktionskoefficient is the same for both the objects)
 
  • #6
BvU
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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



Homework Equations



The Attempt at a Solution

 
  • #7

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

Homework Equations


ω1/ω2=√r2/r1
V=ωr

The Attempt at a Solution



√r2/r1 * ω1/ω2=0

√((ω1r2)/(ω2r1))=0

hmm this doenst feel right..
 
  • #8
Dick
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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

Homework Equations


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?
 
  • #9
BvU
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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 =


The Attempt at a Solution



...
 
  • #10

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?
 
  • #11
Dick
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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.
 
  • #12

The Attempt at a Solution


F = m·v2/r = (m* (ωr)2)/r
ac =v2/r =(ωr)2/r
 
  • #13
Dick
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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.
 
  • #14
agree
(ωr)2/r = 2ω3r2
 
  • #15
Dick
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agree
(ωr)2/r = 2ω3r2
I don't recognize the algebra you did you get that. Can you explain?
 
  • #16
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:
  • #17
or the potens rule axbx=(ab)x
 
  • #18

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]
 
  • #19
Dick
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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##.
 
  • #20

The Attempt at a Solution



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

I Think i got it right ?!
 
  • #21
Dick
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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!
 
  • Like
Likes SwedishFred
  • #22
Thanks alot sir!
we will meet again ;-)
best regards
Fredrik
 

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