Acceleration in Polar Coords, Intuitive Definition video

In summary, acceleration in polar coordinates is the rate of change of polar velocity and takes into account both speed and direction. It differs from acceleration in Cartesian coordinates by considering the direction of motion and using radial and tangential components. The formula for calculating acceleration in polar coordinates is a = (v^2)/r + v(dθ/dt). Understanding this concept can be useful in real-world applications such as satellite orbits and roller coaster design. However, there are limitations to using polar coordinates, such as being limited to two-dimensional motion and not accounting for external forces. Conversion between polar and Cartesian coordinates can also be complex.
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Summary:: I wish this video (and YouTube in general) was around when I took intermediate level mechanics as an undergraduate physics student:

I wish this video (and YouTube in general) was around when I took intermediate level mechanics as an undergraduate physics student:

 
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I'm impressed that the lecturer can print so neatly using a mouse. (Or maybe a touchpad?)
 
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The lecturer is probably using a stylus.
 

FAQ: Acceleration in Polar Coords, Intuitive Definition video

What is acceleration in polar coordinates?

Acceleration in polar coordinates is a measure of how quickly and in which direction the velocity of an object is changing at a given point in time. It takes into account both the magnitude and direction of the velocity vector.

How is acceleration in polar coordinates different from acceleration in Cartesian coordinates?

The main difference between acceleration in polar coordinates and Cartesian coordinates is the way in which the coordinates are represented. In polar coordinates, the position of an object is described using a distance from the origin (r) and an angle from a reference line (θ), while in Cartesian coordinates, the position is described using x and y coordinates. As a result, the equations for acceleration in polar coordinates are different from those in Cartesian coordinates.

How is acceleration calculated in polar coordinates?

To calculate acceleration in polar coordinates, you first need to determine the radial and tangential components of the acceleration. The radial component is the acceleration in the direction of the radius, while the tangential component is the acceleration in the direction of the tangent to the circle at a given point. These components can then be combined using vector addition to find the total acceleration.

What is the intuitive definition of acceleration in polar coordinates?

The intuitive definition of acceleration in polar coordinates is the rate of change of the velocity vector as an object moves along a circular path. It takes into account both the change in speed and the change in direction of the object's motion.

How is acceleration in polar coordinates used in real-world applications?

Acceleration in polar coordinates is used in a variety of real-world applications, such as in the design of roller coasters and other amusement park rides, in the analysis of planetary motion, and in the study of fluid dynamics. It is also commonly used in navigation and control systems for vehicles and aircraft.

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