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Alright, the problem here is that I seem unable to grasp an example given in class. I am not sure if this is due to not copying it down correctly, or if there's something I am just missing. Either way, I know I am not the only one who has had a bit of trouble with this. I'm hoping that someone with a greater knowledge of physics can spot what is going on.

Bead threaded on a smooth rod (i.e. no friction) which rotates with constant angular velocity [tex]\omega[/tex] about one end. Investigate the motion.

Where r is a radial vector,

[tex]\dot{r}[/tex]=0, [tex]\dot{\theta}[/tex]=[tex]\omega[/tex], and r=r[tex]_{0}[/tex] at t=0

The dot above the letters and symbols, as far as I am aware, just denotes the first derivative (in case this isn't a standard notation of some sort). Also, the subscript doesn't seem to be working in the preview, so in case it does not turn out right, that is meant to be a subcript zero, not r^0. It's just denoting a particular distance up the rod that the bead is.

Now this is the working out that I copied.

Newtons second law:

[tex]\ddot{r}[/tex] -r[tex]\dot{\theta}[/tex]^2 = 0.

(I realise Newton's second law should include a multiplication by mass, but I'm just writing the information I have). r dot dot is the second derivative I believe.

[tex]\theta[/tex] = [tex]\omega[/tex]t

[tex]\dot{\theta}[/tex] = [tex]\omega[/tex] ; [tex]\ddot{r}[/tex] = [tex]\omega[/tex]*r[tex]^{2}[/tex]

Solutions:

e^wt and e^-wt

Oh, the omega is not meant to be superscript throughout the question by the way, I don't know why it is; and the w in the 'solution' represents an omega. So it is e to the power of omega*time.

All I need to know is what on Earth the solutions are for and how did they materialise?

EDIT: I really made a mess of this whole latex thing.

## Homework Statement

Bead threaded on a smooth rod (i.e. no friction) which rotates with constant angular velocity [tex]\omega[/tex] about one end. Investigate the motion.

Where r is a radial vector,

[tex]\dot{r}[/tex]=0, [tex]\dot{\theta}[/tex]=[tex]\omega[/tex], and r=r[tex]_{0}[/tex] at t=0

The dot above the letters and symbols, as far as I am aware, just denotes the first derivative (in case this isn't a standard notation of some sort). Also, the subscript doesn't seem to be working in the preview, so in case it does not turn out right, that is meant to be a subcript zero, not r^0. It's just denoting a particular distance up the rod that the bead is.

## Homework Equations

Now this is the working out that I copied.

Newtons second law:

[tex]\ddot{r}[/tex] -r[tex]\dot{\theta}[/tex]^2 = 0.

(I realise Newton's second law should include a multiplication by mass, but I'm just writing the information I have). r dot dot is the second derivative I believe.

## The Attempt at a Solution

[tex]\theta[/tex] = [tex]\omega[/tex]t

[tex]\dot{\theta}[/tex] = [tex]\omega[/tex] ; [tex]\ddot{r}[/tex] = [tex]\omega[/tex]*r[tex]^{2}[/tex]

Solutions:

e^wt and e^-wt

Oh, the omega is not meant to be superscript throughout the question by the way, I don't know why it is; and the w in the 'solution' represents an omega. So it is e to the power of omega*time.

All I need to know is what on Earth the solutions are for and how did they materialise?

EDIT: I really made a mess of this whole latex thing.

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