chart2006
Feb24-09, 10:29 PM
1. The problem statement, all variables and given/known data
The two-dimensional motion of a particle is defined by the relationship r = \frac {1}{sin\theta - cos\theta} and tan\theta = 1 + \frac {1}{t^2} , where r and \theta are expressed in meters and radians, respectively, and t is expressed in seconds. Determine (a) the magnitudes of velocity and acceleration at any instant, (b) the radius of curvature of the path.
2. Relevant equations
r = \frac {1}{sin\theta - cos\theta}
tan\theta = 1 + \frac {1}{t^2}
3. The attempt at a solution
I've made a few attempts but they seem way more complicated than the problem should be I think. I'm assuming I need to solve tan\theta for \theta . Once i've done that I figure I'd need to differentiate both r and \theta to find \dot{r}, \ddot{r}, \dot{\theta}, \ddot{\theta}.
I don't know if I'm on the correct route but any help would be appreciated. thanks!
The two-dimensional motion of a particle is defined by the relationship r = \frac {1}{sin\theta - cos\theta} and tan\theta = 1 + \frac {1}{t^2} , where r and \theta are expressed in meters and radians, respectively, and t is expressed in seconds. Determine (a) the magnitudes of velocity and acceleration at any instant, (b) the radius of curvature of the path.
2. Relevant equations
r = \frac {1}{sin\theta - cos\theta}
tan\theta = 1 + \frac {1}{t^2}
3. The attempt at a solution
I've made a few attempts but they seem way more complicated than the problem should be I think. I'm assuming I need to solve tan\theta for \theta . Once i've done that I figure I'd need to differentiate both r and \theta to find \dot{r}, \ddot{r}, \dot{\theta}, \ddot{\theta}.
I don't know if I'm on the correct route but any help would be appreciated. thanks!