### Newton’s Law in Polar Coordinates Lecture 6

Newton’s Laws of Motion can be expressed in various coordinate systems, one of which is the polar coordinate system. Polar coordinates are particularly useful in problems involving circular or rotational motion, where the use of Cartesian coordinates (x, y) might be cumbersome. In polar coordinates, a position is described by the radial distance r from the origin and the angular coordinate θ which is the angle measured from a reference direction.

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### Example: Planetary Motion

In planetary motion, the gravitational force is a central force, and the equations of motion in polar coordinates can be used to derive Kepler’s laws of planetary motion.

In summary, expressing Newton’s Laws in polar coordinates provides a powerful framework for solving problems involving rotational or circular motion, where the motion is naturally described in terms of radial and angular components.