---
tags : Mechanics,Kinematics
title : 2020.4.4(6)
---
# Mechanics(6)
## §1.4 Plane polar coordinate component on two dementional space
### 1.4.1 Polar coordinate component of velocity
Write a movement of point in place by polar coordinate **r** = (r(t) , $\theta$(t)).
Think about polar coordinate component of this point's velocity and acceleration.

First , set an unit bector **e**~r~ which exists radial direction.

Write the position of the object.
#### **r** = r**e**~r~

Differentiate this for making velocity

#### $\large v$ = $\large \frac{d\bf r}{dt}$ = $\large \frac{d}{dt}r\bf e$~r~ = $\large \frac{dr}{dt}\bf e$~r~ + r$\large\frac{d{\bf e}r}{dx}$

Clause 1 means the effect of changing arm length to radical direction.
Clause 2 means the effect of the degree of arm spinning and its "arm length" times.