Polar Coordinates

 

In some problems with circular symmetry, it is easier to formulate Newton’s laws of motion in a coordinate system that has the same symmetry. ¬†Here we derive equations for velocity and acceleration in polar coordinates and then we solve a few problems.

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An Intuitive Derivation of the Velocity Equation

Here we define polar coordinates and derive an expression for velocity. The derivation is mostly intuitive. We’ll do the rigorous derivation later. If you’re having difficulty playing this video, you may find the Youtube version here.

An Intuitive Derivation of the Acceleration Equation

There are even more terms in the equation for acceleration. Here we try to think about what they mean. If you are not able to play the video below, you may access the YouTube version here.

Mathematical Derivation of Velocity and Acceleration

Finally, we derive expressions for velocity and acceleration using the definition of derivative, the product rule, and chain rule. If you are having difficulty playing the video below, you may find the YouTube version here.