# Homework Help: Angle of a F*r calculation

1. Mar 16, 2008

### AnkhUNC

1. The problem statement, all variables and given/known data

Force F= (-6.93 N) + (7.85 N) acts on a particle with position vector r = (4.66 m) + (1.36 m). What are (a) the magnitude of the torque on the particle about the origin and (b) the angle between the directions of and ?

2. Relevant equations

3. The attempt at a solution

So I find (a) to be 46.0058 N*m which is correct and for (b) I use t/f*r

So 46.0058/sqrt(6.93^2+7.85^2)*sqrt(4.66^2+1.36^2) = .9050610046

sin-1(of that) = 64.8315006 = angle. But this is incorrect?

2. Mar 16, 2008

### G01

Remember this definition of the dot product?

$$\vec{A}\cdot\vec{B}=|A||B|\cos\theta$$

Try using this to solve for the angle and see if it gives the same value. (I think the cross product formula should work, but for some reason I'm getting a different value for the angle in each one...)

3. Mar 16, 2008

### AnkhUNC

Does that work with a vector? I've been using t = rFsin(Theta)

4. Mar 16, 2008

### AnkhUNC

Only thing I could think of is maybe its in the wrong quadrant but that doesn't seem to be the problem.

5. Mar 16, 2008

### G01

Yes. It's the formula for the dot product between two vectors. Theta is the angle between the vectors.

Also, you have to know that:

$$\vec{A}\cdot\vec{B}=A_xB_x+A_yB_y$$

in order to use the dot product formula to find the angle between the vectors.

Let A=F and B=r and see what angle the dot product formula gives you.

(Sorry if you haven't learned what I'm talking about here. I also got the same angle you did with the formula your using. So I'm trying to check that answer with another equation.)

6. Mar 16, 2008

### AnkhUNC

Really appreciate the help, not sure what its looking for :(

7. Mar 16, 2008

### G01

Well. I think the method your using should be correct. Here is what I suggest.

If your answer for the torque is correct, and the angle you get from the torque formula is wrong, I suggest the following alternative method:

Find the angle of the F vector from the x axis. (You should be able to do this using the components.)

Do the same for the r vector.

Now you should be able to subtract the two angles to find the angle between them.