Lecture 6: Velocity, acceleration, and Kepler's second law.
In this lesson on velocity, acceleration, and Kepler's Second Law, we learn about the use of parametric equations to describe the motion of a point in the plane or space as a function of time or a parameter that tracks progress. We explore concepts like speed, represented as a scalar quantity and velocity, represented as a vector. The unit tangent vector to the trajectory is also introduced, along with the concept of arc length, which is the distance traveled along the trajectory. The lesson offers insight into how these concepts relate to one another, and how they can be used to analyze the motion of a point in more detail.
Learn more about parametric equations and how they pertain to velocity, acceleration, and Kepler's Law.
Denis Auroux. 18.02 Multivariable Calculus, Fall 2007. (Massachusetts Institute of Technology: MIT OpenCourseWare). http://ocw.mit.edu (Accessed March 15, 2009). License: Creative Commons Attribution-Noncommercial-Share Alike.
- Lecture Notes - Lecture Notes from this lesson.
- Transcript of Lesson - Written transcript from this lesson.
- Problem Set - A problem set with some problems from this lecture.
- How can you describe the position of a point moving along a cycloid using parametric equations?
- How can you find the position vector of a moving point?
- How can you find the velocity of a moving point using vectors?
- What is the formula for vector acceleration?
- How can you find arc length using vectors?
- What is the arc length formula in Calculus?
- How do you find the length of an arch of a cycloid?
- What is a unit tangent vector?
- What does Kepler's second law have to do with vectors?
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Staff Review
This lesson is all about velocity and acceleration of moving particles, picking up from where the previous video left off with parametric equations and cycloids. Obviously, speed and acceleration are important concepts in Calculus, so this lesson is quite important. Also, a very interesting application using Keplerâs second law is explained in this lesson. -
