Dipole Oscillation: Solving for Period

[learningphysics]

sorry, those are the y-componets since the y-componets is the force that the torque considers.

But there is no y-component... I think you mean the component perpendicular to the dipole line?

It is easier to take torque here as the force (horizontal)... times the perpendicular distance from the axis of rotation to the line of force... ie rsintheta is the perpendicular distance the the line of force (where the force is horizontal)... hence torque if Frsin(theta)...

 

[indigojoker]

yeah, i mean the F in my drawing is =rsintheta

does my explanation in the pdf make more sense now?

 

[learningphysics]

yeah, i mean the F in my drawing is =rsintheta

does my explanation in the pdf make more sense now?

I'm still finding it confusing... stick with a particular definition for alpha and theta... for example alpha as the clockwise angular acceleration... theta is the angle measured from the positive x-axis... taking positive as counterclockwise... negative as counterclockwise...

Define theta and alpha in a certain way of your choosing... but then stick with that...

Same way... stick with a particular direction for torque... ie clockwise positive, counterclockwise negative...

with the definitions I chose above (alpha clockwise angular acceleration... theta measured from positive x-axis counterclockwise):

clockwise torque = I* alpha, and alpha = $$-\frac{d^2\theta}{dt^2}$$

these two definitions don't change...

in the first case clockwise torque =Frsin(theta).

in the second case also, clockwise torque = Frsin(theta) (see sintheta is negative because theta is negative... and the number comes out negative because it's rotating the other way... but it is still the clockwise torque... the clockwise torque comes out negative... counterclockwise torque is positive).

The definitions don't change... the equations don't change... the numbers come out different but the relationships remain the same...

 

[indigojoker]

ok, let's see if i understood it this time:
http://home.earthlink.net/~suburban-xrisis/phy.pdf

 

[learningphysics]

ok, let's see if i understood it this time:
http://home.earthlink.net/~suburban-xrisis/phy.pdf

The first part looks essentially right... but I don't like how you just went from torque = -I$$\frac{d^2\theta}{dt^2}$$ to substituting in $$-\frac{d^2\theta}{dt^2}$$ for $$\frac{d^2\theta}{dt^2}$$

I think it's better to just say that since $$\frac{d^2\theta}{dt^2}$$ is negative, torque = -I$$\frac{d^2\theta}{dt^2}$$ comes out positive... which is consistent with the torque being clockwise.

For the second part, I'd just write torque = -I$$\frac{d^2\theta}{dt^2}$$, is still valid... because $$\frac{d^2\theta}{dt^2}$$ is positive... giving a negative value for the torque... and this is consistent with the fact that torque is counterclockwise here... so we expect a negative value.