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In this module, we will expand our study of Kinematics to multi-dimensional motion. While we could make a linear motion problem that we have studied previously into a multi-dimensional motion problem by rotating our coordinate axis so that the object doesn’t move along any of the coordinate axes, this is not usually done by physicists as it makes the math harder.

Motion along a curved path with our present level of math skills requires us to deal with multi-dimensional motion. We will deal in detail with two special cases: projectile motion and circular motion.

For those students who decide to go on to more advanced study at a university, you will discover in your advanced physics and math courses that there are additional coordinate systems (curvilinear coordinates) besides just polar coordinates that can simplify more complicated curved motion into simpler one dimensional or multidimensional problems.

In this module, we will examine two of the most important concepts in physics, Work & Kinetic Energy. These two concepts are linked by the Work-Energy Theorem which connects our previous work on Newton’s Laws to an even more general and powerful solution technique for solving physics problems called Energy Analysis. Prior to starting this module, you will need to review the math that we will be using which is called the Dot Product. This material is in the Vector Module.

The center-of-mass is the location in space that obeys Newton’s Laws for the motion of an extended object. It is extremely important when analyzing the motion or stability of real-world objects like the human body or a bridge. It also plays an important roll in doing energy analysis of objects that undergo general motion (both rotation and translation).