Plane Curvilinear Motion - Polar Coordinates - Example 3.4-2

 

For the following situations, write an expression for the velocity and acceleration in polar coordinates.

 

v = (dr/dt)e_r + r(dθ/dt)e_θ

 

a = ((d ²r/dt ²) - r(dθ/dt)²)e_r + (r(d ²θ/dt ²) + 2(dr/dt)(dθ/dt))e_θ

 

• A car traveling on a circular track.  

 



 

 

 

• A car on a Ferris wheel turning at a constant rate.  

 



 

 

 

• Body A held by the end of an articulating robotic arm.