# Uniform Circular Motions

1. Oct 1, 2004

### HeRo

I thought I had this problem on lock, but apparently I was wrong in my methods. My original answer was 7.97i + 3.92j but that is incorrect. I've tried other methods but now I'm just lost. I need some assistance or I'm a dead man.

"A particle is in uniform circular motion about the origin of an xy coordinate system, moving counterclockwise with a period of 8.00 s. At one instant, its position vector (from the origin) is r = (6.00 m) i - (5.00 m) j. At that instant, what is its velocity in unit-vector notation?"

2. Oct 1, 2004

### Tide

There are several ways of approaching this one.

Since you know the position at one instant and the particle is orbiting the origin you can determine the radius of the orbit and, therefore, the circumference of the orbit. Divide the circumference by the period to find the speed.

Now just find a unit vector in the plane and perpendicular to the position vector, multiply by the speed and you have the result you need. Just be sure to pick the unit vector so that the motion is counterclockwise.

A second approach is to write the position vector as
$$\vec r = r (\cos (\omega t + \phi) \hat i + \sin (\omega t + \phi) \hat j$$
and use the data provided to determine $\phi$ and r.