How Do You Calculate the Acceleration of a Particle in Polar Coordinates?

[toastie]

Homework Statement

A particle moves in a plane with constant radial velocity (r dot) and constant angular velocity (theta dot). When the particle is at distance r from the origin, determine the magnitude of the acceleration.

r dot = 4.3 m/s
theta dot = 2.5 rad/s
r = 3.1 m
speed of the particle at r = 8.86 m/s

Homework Equations

v = (((r dot)^2)+((r*(theta dot))^2))^.5

The Attempt at a Solution

I have attempted to find the derivative of the above equation, but I am not sure if I am doing the derivate wrong.

 

[Andrew Mason]

Homework Statement

A particle moves in a plane with constant radial velocity (r dot) and constant angular velocity (theta dot). When the particle is at distance r from the origin, determine the magnitude of the acceleration.

r dot = 4.3 m/s
theta dot = 2.5 rad/s
r = 3.1 m
speed of the particle at r = 8.86 m/s

Homework Equations

v = (((r dot)^2)+((r*(theta dot))^2))^.5

You have the right expression for the magnitude of v as a function of r. Take the derivative with respect to time. Since $\dot r$ is constant with time, what is its derivative?

$$|a| = |dv/dt| = \frac{d}{dt}\sqrt{|\dot r|^2 + \omega^2r^2}$$

AM

 

[toastie]

thanks for the help