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Chapter 4
Motion in Two or Three Dimensions

Position and Displacement Vectors
To describe the motion of an object, one should first be able to describe its position (where it is at any particular time). More precisely, the…
Average and Instantaneous Velocity Vectors
To calculate other physical quantities in kinematics, the time variable must be introduced. The time variable not only allows us to state where an…
Acceleration Vectors
In everyday conversation, accelerating means speeding up. Acceleration is a vector in the same direction as the change in velocity, Δv,…
Direction of Acceleration Vectors
Acceleration occurs when velocity changes in magnitude (an increase or decrease in speed), direction, or both. Although acceleration is in the…
Projectile Motion
An object thrown in the air follows a parabolic path under the influence of Earth's gravitational force. The motion of such an object is called…
Projectile Motion: Equations
Projectile motion is commonly observed in our day-to-day life. For example, a basketball thrown by a player, an arrow shot from a bow, and kids…
Projectile Motion: Example
The theory of projectile motion is very useful for players of several sports to improve their performance. For example, a javelin thrower needs to…
Uniform Circular Motion
Uniform circular motion is a specific type of motion in which an object travels in a circle with a constant speed. For example, any point on a…
Non-uniform Circular Motion
In uniform circular motion, the particle executing circular motion has a constant speed, and the circle is at a fixed radius. However, not all…
Relative Velocity in One Dimension
The understanding of the concept of reference frames is essential to discuss relative motion in one or more dimensions. When we say that an object…
Relative Velocity in Two Dimensions
Relative velocity is the velocity of an object as observed from a particular reference frame, or the velocity of one reference frame with respect to…
Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow
3D-PTV is a quantitative flow measurement technique that aims to track the Lagrangian paths of a set of particles in three dimensions using…
Visualization of High Speed Liquid Jet Impaction on a Moving Surface
Two apparatuses for examining liquid jet impingement on a high-speed moving surface are described: an air cannon device (for examining surface speeds…
Preparation and 3D Tracking of Catalytic Swimming Devices
We report a method to prepare catalytically active Janus colloids that "swim" in fluids and describe how to determine their 3D motion using…

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