- #1

Like Tony Stark

- 179

- 6

- Homework Statement
- A particle moves in a plane trajectory such that its polar coordinates depend on time according to ##r=0.833t^3+5t## and ##\theta=0.3t^2## where ##r## is measured in ##cm##, ##\theta## in ##rad## and ##t## in seconds. Determine the magnitude of the velocity and acceleration and the radius of curvature at ##t=2##.

- Relevant Equations
- ##a_n=\frac{v^2}{\rho}##

Well, what I've done so far is calculating the magnitude of velocity and acceleration replacing ##t=2## in ##\theta (t)## and ##r(t)## so I could get the expressions for ##\dot r##, ##\dot \theta##, ##\ddot r## and ##\ddot \theta##. But that's not my problem... my problem is related to the radius of curvature... how can I do it? In previous exercises where I was given an image of the situation I wrote the acceleration (written in terms of radius and theta) in terms of the tangent and normal vector so that I had the normal acceleration and I could use ##a_n=\frac{v^2}{\rho}##, but now I don't have any image to know how to decompose the acceleration in the normal and tangent components.