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College Physics

Introduction to Two-Dimensional Kinematics

College PhysicsIntroduction to Two-Dimensional Kinematics

In this figure the Dragon Khan rollercoaster in Spain’s Universal Port Aventura Amusement Park is shown. There are mostly curved paths in the rollercoaster. Near to the rollercoaster there is the track of rollercoaster cart under a bridge. There are some trees near the track.
Figure 3.1 Everyday motion that we experience is, thankfully, rarely as tortuous as a rollercoaster ride like this—the Dragon Khan in Spain’s Universal Port Aventura Amusement Park. However, most motion is in curved, rather than straight-line, paths. Motion along a curved path is two- or three-dimensional motion, and can be described in a similar fashion to one-dimensional motion. (credit: Boris23/Wikimedia Commons)

Chapter Outline

3.1 Kinematics in Two Dimensions: An Introduction
  • Observe that motion in two dimensions consists of horizontal and vertical components.
  • Understand the independence of horizontal and vertical vectors in two-dimensional motion.
3.2 Vector Addition and Subtraction: Graphical Methods
  • Understand the rules of vector addition, subtraction, and multiplication.
  • Apply graphical methods of vector addition and subtraction to determine the displacement of moving objects.
3.3 Vector Addition and Subtraction: Analytical Methods
  • Understand the rules of vector addition and subtraction using analytical methods.
  • Apply analytical methods to determine vertical and horizontal component vectors.
  • Apply analytical methods to determine the magnitude and direction of a resultant vector.
3.4 Projectile Motion
  • Identify and explain the properties of a projectile, such as acceleration due to gravity, range, maximum height, and trajectory.
  • Determine the location and velocity of a projectile at different points in its trajectory.
  • Apply the principle of independence of motion to solve projectile motion problems.
3.5 Addition of Velocities
  • Apply principles of vector addition to determine relative velocity.
  • Explain the significance of the observer in the measurement of velocity.

The arc of a basketball, the orbit of a satellite, a bicycle rounding a curve, a swimmer diving into a pool, blood gushing out of a wound, and a puppy chasing its tail are but a few examples of motions along curved paths. In fact, most motions in nature follow curved paths rather than straight lines. Motion along a curved path on a flat surface or a plane (such as that of a ball on a pool table or a skater on an ice rink) is two-dimensional, and thus described by two-dimensional kinematics. Motion not confined to a plane, such as a car following a winding mountain road, is described by three-dimensional kinematics. Both two- and three-dimensional kinematics are simple extensions of the one-dimensional kinematics developed for straight-line motion in the previous chapter. This simple extension will allow us to apply physics to many more situations, and it will also yield unexpected insights about nature.

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