How Do You Calculate the X-Coordinate of a Particle in Circular Motion?

[Cate]

Homework Statement

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

Homework 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?

 

[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.

 

[Cate]

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

 

[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...

 

[cepheid]

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).

 

[Cate]

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

 

[edziura]

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

 

[cepheid]

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

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)?

 

[Cate]

-5.86

 

[Cate]

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