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Newton's Second Law & Uniform Circular Motion

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  • 0:01 Newton's Second Law Spun
  • 0:56 The Formula
  • 1:46 Explaining It In Plain English
  • 3:44 Examples
  • 4:57 Lesson Summary
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Lesson Transcript
Instructor: Kevin Newton

Kevin has edited encyclopedias, taught middle and high school history, and has a master's degree in Islamic law.

Sure, Newton's Second Law of Motion works well in one dimension, but what happens when you put it on a curve? In this lesson, we'll see how the Second Law applies with respect to Uniform Circular Motion.

Newton's Second Law Spun

By now, you're probably pretty familiar with Newton's Second Law of Motion, the one that says that force is equal to mass times acceleration. You've seen how a bullet accelerating at a very fast rate can do as much damage as a spear, with a much greater mass, that has a much lower acceleration. However, what's with that word 'acceleration?' Can't we just say 'velocity?' Unfortunately, it's not that easy. One of the main reasons that it isn't so simple is because once we apply Newton's Second Law to motion, velocity is constantly changing. In other words, for us to be able to explain what is going on, we have to use acceleration. In this lesson, we're going to do exactly that, explaining how Newton's Second Law of Motion explains what is called uniform circular motion. Uniform circular motion is the act of motion in a circle around a very precise point.

The Formula

Usually, when we use Newton's Second Law, the a for acceleration is pretty easy to define. More often than not, it is in terms of meters per second squared in a given direction, or some other similar unit. However, because we're moving around a circle, we need a different way to find the acceleration. Otherwise, we'd be stuck defining a new direction every millisecond. To get over this, we state that acceleration is equal to the speed squared divided by the radius. This can also be found by squaring the angular speed and multiplying it by the radius, depending on what information you have available. We simply plug that new number into our usual equation, meaning that now F is equal to m, for mass, times s for speed, squared, divided by r, for radius.

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