# Finding the Angle Between Two Forces

1. Mar 3, 2013

### Astrum

1. The problem statement, all variables and given/known data
Question is in the attachment

2. Relevant equations

3. The attempt at a solution

I understand the concept and ideas, but the geometry evades me.

In polar coordinates, we have two components, $\hat{r},\hat{\theta}$

I know that you just integrate the dot product of $\vec{F}$ and $d\vec{r}$ with the boundaries of position, but how did we find the angle between the two vectors?!

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2. Mar 3, 2013

### Simon Bridge

... the question in the attachment is:
"What is the velocity of m when the rod is at angle $\phi$?"
... which is answered in the rest of the attachment.

The geometry is circular. They drew you a diagram.
Probably what you need to do is redraw the diagram, bigger, for different values of $\phi$ - carefully draw in the vectors, resolve components, and watch how they change.

3. Mar 3, 2013

### Astrum

I should have been clearer. I know the concept behind the problem, I know how they solved, just not where they go the [tex]cos(\varphi-\frac{\pi}{2}[itex]

That perplexes me. The dot product equals the magnitude of each vector multiplied by each other, times the cos of the angle between them.

I don't know how they determined the angle.

4. Mar 3, 2013

### TSny

Can you show that the two angles marked θ in the picture are equal? [EDIT: The dotted line is horizontal]

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5. Mar 3, 2013

### Simon Bridge

... that is why I suggested you draw out the bigger diagrams. The exercise of resolving components gets you focussed on how the angles are related to each other. TSny has done one for you.

6. Mar 4, 2013

### Astrum

I didn't even realize that those angles were equal.....

I have not a clue how to prove they're equal.

7. Mar 4, 2013

### TSny

Construct another horizontal auxiliary line through the mass m. Also think about how the vector dr is oriented relative to the rod.