Dynamics Polar Coordinates question

[Marchese_alex]

Hi everyone. I am a little desperated cause my exam is on monday and still much stuff to do.
I don't get when I am supposed to use/consider radial and tranversal forces. Most excercises say "it rotates on the horizontal or vertical" I guess this is the info that tells me if there is radial/tranversal forces but i don't get it. Some time they consider the forces and sometimes they dont. I attach an example

Ps. Please keep it simple cause the profesor isn't that good and basically I am learning by my self
Thanks!

 

[tiny-tim]

Welcome to PF!

Hi Marchese_alex! Welcome to PF!

I don't get when I am supposed to use/consider radial and tranversal forces.

Usually, you have an F = ma equation for each,

but one of them involves an unknown force …

in that case, you have to use the other one!​

in this case, the only radial force is the spring (because there's no friction), and you know what that is, so you can use the radial equation

you can't use the tangential equation because you don't know what the tangential force is (until you work it out from the radial equation!)

 

[Marchese_alex]

Hi Marchese_alex! Welcome to PF!


Usually, you have an F = ma equation for each,

but one of them involves an unknown force …

in that case, you have to use the other one!​

in this case, the only radial force is the spring (because there's no friction), and you know what that is, so you can use the radial equation

you can't use the tangential equation because you don't know what the tangential force is (until you work it out from the radial equation!)

What I've gather from internet(because my profesor never teach us this) is like you say... i will have two forces radial (Fr=ma) in the direction of "r" (according to book) and angular force, that will be tangential to the path or just perpendicular to Fr (Fbeta=ma) correct me if wrong. If i see that the object angel changes I say that there's an angular force. For example, if the rod goes from horizontal (flat on floor) to vertical, i can say that a angular force is present. Correct?

And since there's a change in angle it will be going in a circular motion, and if there's a circular motion I have a centripetal force. Is that is the same thing as radial force or is the samething as radial aceleration(Ar)--> Fr=mAr

 

[tiny-tim]

What I've gather from internet(because my profesor never teach us this) is like you say... i will have two forces radial (Fr=ma) in the direction of "r" (according to book) and angular force, that will be tangential to the path or just perpendicular to Fr (Fbeta=ma) correct me if wrong.

correct, but confusing

there are two F = ma equations, one radial and one tangential

(essentially, there's only one F = ma vector equation, of which you can take the components in any two independent directions, which you usually take to be perpendicular)​

there may be two forces, or more than two forces, it's the number of equations that matters

If i see that the object angel changes I say that there's an angular force. For example, if the rod goes from horizontal (flat on floor) to vertical, i can say that a angular force is present. Correct?

if the angel accelerates then yes, there must be a force in the tangential direction

(but if the angle changes uniformly, no)

And since there's a change in angle it will be going in a circular motion, and if there's a circular motion I have a centripetal force.

correct

(even if the angle changes uniformly)

except you really ought to call it centripetal acceleration, and not mention centripetal force unless you're using a rotating frame of reference

Is that is the same thing as radial force or is the samething as radial aceleration(Ar)--> Fr=mAr

if there is angular motion, then there is always a centripetal acceleration

this is separate from the radial acceleration, which is d²r/dt²…

you must subtract the centripetal acceleration (because it's always negative ) from the radial acceleration to get the total "a" to put in the radial F = ma ​

 

[tiny-tim]

to illustrate the last point, try this problem …

a smooth rod rotates uniformly and horizontally with angular velocity ω

a bead is free to slide (without friction) on the rod … obviously, it will move away from the centre!

but the only force on it (there's no spring or anything else) is the normal force from the rod, which is tangential …

so why does it have a radial motion, and what is the equation? ​

 

[Marchese_alex]

if the angel accelerates then yes, there must be a force in the tangential direction

(but if the angle changes uniformly, no)


if there is angular motion, then there is always a centripetal acceleration

this is separate from the radial acceleration, which is d²r/dt²…

you must subtract the centripetal acceleration (because it's always negative ) from the radial acceleration to get the total "a" to put in the radial F = ma ​

[/QUOTE]


When you say substract centripetal acceleration you mean ~~> see part III picture

Is my diagram correct? Is radial force(Fr) always in that direction?

http://i174.photobucket.com/albums/w105/marchese_alexander/cd953eb0b2ce1c91d11cce442007042f.jpg

 

[tiny-tim]

When you say substract centripetal acceleration you mean ~~> see part III picture

yes, the radial component of acceleration is always a_r = r'' - r(θ')²

r'' is what i call the radial acceleration (i don't know whether other people call it that, or whether they call the whole of a_r the radial acceleration)

and r(θ')² is the centripetal acceleration

Is my diagram correct? Is radial force(Fr) always in that direction?

there isn't necessarily a radial force

for example, if a weight on a string attached to the ceiling moves in a horizontal circle, the only forces are vertical (the weight) and along the string (the tension) …

but the radial direction is horizontal ​

 

[Marchese_alex]

What exactly make this excercises different that they say Fr exist?

 

[tiny-tim]

no, they don't call it the radial force, they call it the radial component of the force

the (net) force always has a radial component,

but there isn't always an individual force along the radial direction ​

 

[Marchese_alex]

for example, if a weight on a string attached to the ceiling moves in a horizontal circle, the only forces are vertical (the weight) and along the string (the tension) …

but the radial direction is horizontal ​

and since there angular motion I will have centripetal acceleration. Right?

 

[Marchese_alex]

Ok i get the centri acceleration. Now i just don't get
1.the radial and tranversal component part of a force... Is it radial for "x" component and tranversal for y

2.what exactly is F and Fr representing in the free body diagram

 

[tiny-tim]

and since there angular motion I will have centripetal acceleration. Right?

Right!

Ok i get the centri acceleration. Now i just don't get
1.the radial and tranversal component part of a force... Is it radial for "x" component and tranversal for y

2.what exactly is F and Fr representing in the free body diagram

In the diagram, "F" seems to be a mistake for "F_θ".

The problem asks for the "radial and transverse components of the force exerted on A", which are F_r and F_θ.

Radial is the r component, and transverse is the θ component.

(tangential isn't often used, it's the component of the force along the line of motion, which won't be transverse unless r is constant)

 

[Marchese_alex]

Right!


In the diagram, "F" seems to be a mistake for "F_θ".

The problem asks for the "radial and transverse components of the force exerted on A", which are F_r and F_θ.

Radial is the r component, and transverse is the θ component.

(tangential isn't often used, it's the component of the force along the line of motion, which won't be transverse unless r is constant)

Got it!

 

[Marchese_alex]

How about this excercise.

The only part I don't get is why I can't say that the first derivative of the angle is 0 and they put that is w(angular velocity). I know that the first derivative is angular velocity and the second derivative is angular acceleration. Also I know if I say is 0 then I would not be able to find what the excercise is asking. I am just trying to understand the "why".


Heres my data http://i174.photobucket.com/albums/w105/marchese_alexander/5ce37c38be157e984f3f113fe1a3a65f.jpg

 

[tiny-tim]

… why I can't say that the first derivative of the angle is 0 and they put that is w(angular velocity).

θ' is the angular velocity, ω (same as x' is the ordinary velocity, v)

i don't understand why you think ω = 0

if it's moving, then its speed isn't 0, and its angular speed isn't 0

 

[Marchese_alex]

θ' is the angular velocity, ω (same as x' is the ordinary velocity, v)

i don't understand why you think ω = 0

if it's moving, then its speed isn't 0, and its angular speed isn't 0

Ok! Thanks

 

[Marchese_alex]

How about this case...

Why in excercice ( 14.94) its wrong to say Fr-mgsin(angle)=m(bla bla) and rigth to say Fr=m(bla bla). Or symply put why the weight is not being considered?

Whats the difference in this excercice ( 14.96) that they consider "mg"excercise #94 http://i174.photobucket.com/albums/w105/marchese_alexander/920ed870e3bafe05a9a5912d0708bd7c.jpg

Excercise #96 http://i174.photobucket.com/albums/w105/marchese_alexander/9eb8ff403a1639780777f933754f7630.jpg

 

[Marchese_alex]

Bump... Need to know please

 

[tiny-tim]

Why in excercice ( 14.94) its wrong to say Fr-mgsin(angle)=m(bla bla) and rigth to say Fr=m(bla bla). Or symply put why the weight is not being considered?

Whats the difference in this excercice ( 14.96) that they consider "mg"

14.94 is in the x-y plane (ie horizontal)

 

[Marchese_alex]

14.94 is in the x-y plane (ie horizontal)

What do you mean? Still dumb lol

The #95 #97 (can see in pictures) they don't say anything about x,y plane and they put it the same way

 

[tiny-tim]

14.96 obviously includes gravity, from the main diagram

the others don't mention gravity (and 14.95 makes it clear that the plane is horizontal, and asks for the horizontal force)

 

[Marchese_alex]

thats what I don't understand, when you say horizontal. What does horizontal mean? What information it let's me know?

 

[Marchese_alex]

14.96 obviously includes gravity, from the main diagram

the others don't mention gravity (and 14.95 makes it clear that the plane is horizontal, and asks for the horizontal force)

do you mean that in a plane the W is not considered and at horizontal (no plane) it is concidered

 

[tiny-tim]

no, they're the same … if the problem is purely horizontal, then gravity isn't considered either

(i wouldn't worry … exam questions are very clearly worded, even if book examples sometimes aren't )