# Circular Motion of a Particle

1. Sep 19, 2008

### Cate

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

The circular motion of a particle in the x-y plane is given by the equations: r(t)= 6.46 m, theta (t)= (6.96 rad/s) t, where r is the distance from the origin and theta is the polar angle measured counterclockwise from the positve x-axis. Calculate the x-coordinate of the particle at time t= 4.00s

2. Relevant equations

I can visualize it, but can't put the steps togather to solve it. I know I have to find out what angle the position vector is pointing at, then solve for t. The distance from the center of the point probably won't vary with t right?

2. Sep 19, 2008

### edziura

"I can visualize it, but can't put the steps togather to solve it. I know I have to find out what angle the position vector is pointing at, then solve for t. The distance from the center of the point probably won't vary with t right?"

Find theta when t = 4, then use the transformation equation x = r cos theta.

Yes, the particle moves on a circular path around the origin.

3. Sep 19, 2008

### Cate

Thanks for your help! but how do I find theta?

4. Sep 19, 2008

### Cate

Wait I plugged in four or t and got 27.84 for theta which I then plgged into my x= r. cos (theta) formula and got 8.36 m which is not the right answer.....

Last edited: Sep 19, 2008
5. Sep 19, 2008

### cepheid

Staff Emeritus
You made a mistake with the computation of x. You can see that immediately...because your calculated value for the x-coordinate is *greater* than the radius! (That makes absolutely no sense). I would recalculate rcos(theta).

6. Sep 19, 2008

### Cate

I did it agai and got 5.71 which is still wrong...

7. Sep 19, 2008

### edziura

Theta is in radians, not degrees. Check which mode your calculator is in.

8. Sep 19, 2008

### cepheid

Staff Emeritus
That's not very helpful to us. You should POST your work so that we can see if there is some sort of error. In this case, it's a question of punching a few buttons on your calculator and getting the result. There is not much opportunity for error. So here's what I'm going to do. Answer these questions:

1. What is the cosine of 27.84 (IS YOUR CALCULATOR IN RADIAN MODE?)

2. What is r times the cosine of 27.84 (i.e. what is 6.46 * the result of part 1)?

9. Sep 19, 2008

### Cate

-5.86

10. Sep 19, 2008

### Cate

i'm sorry guys i'm really sleep deprived thanks