# Particle moving with radial velocity

1. Sep 11, 2011

### aigerimzh

1. The problem statement, all variables and given/known data
A particle moves in a plane with constant radial r=4m/s. The angular velocity is constant and has magnitude $\Theta$=2rad/s. When the particle is 3m from the origin, find the magnitude of the velocity and the acceleration.

2. Relevant equations

3. The attempt at a solution
The answer is v=root of 52 m/s. But I don't know how to get this number. Can somebody give me a hint?

2. Sep 11, 2011

### pabloenigma

Radial velocity is constant at 4m/s.So when its 3m from origin,the tangential component of velocity is given by v=omega X r, ie 6m/s in this case
Now you have the mutually perpendicular radial and tangential components as 4m/s and 6m/s,calculate the final velocity by vector addition.

3. Sep 11, 2011

### Filip Larsen

As an alternative to calculate speed and acceleration in Cartesian coordinates you may also want to find inspiration in the normal polar equations for velocity and acceleration, see for instance [1]. These equations are more general as they also allow for radial and angular accelerations, but in your case those are zero and inserting that you end up with two simple vector equations to take magnitude of.

[1] http://en.wikipedia.org/wiki/Polar_coordinate_system#Vector_calculus

4. Sep 11, 2011

### aigerimzh

Can I find acceleration by a=v$\Theta$/(1-cos$\Theta$t)?

5. Sep 11, 2011