Displacement
Displacement refers to the net change in position of an object in a specified direction. This concept is crucial in physics as it plays a significant role in calculating average linear and angular velocity, strain, and spring constants. Unlike distance, which measures the total path traveled regardless of direction, displacement accounts for only the initial and final positions, emphasizing directionality. For instance, in a 50-meter race in a 25-meter swimming pool, the distance would be 50 meters, but the displacement could be zero if the swimmer returns to their starting point.
The distinction between distance and displacement is essential, as they often yield different values and meanings. Displacement can be represented in one, two, or three dimensions, and is calculated by subtracting the initial position from the final position. Key applications of displacement include average linear velocity and mechanical work, where displacement influences the calculations of these physical phenomena. Understanding displacement is fundamental for students and professionals in physics and engineering, as it is integral to analyzing motion and mechanical behaviors.
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Displacement
Displacement is an object’s net change in position in a given direction. This is an important concept to understand because it is frequently used in physics to compute average linear or angular velocity, strain, and spring constants. Displacement is computed for linear positions, as well as angular positions.
Distance is a more familiar concept than displacement and students often learn about distance before displacement. The two measures are related, and in specific situations can be equal, but their distinction is important to understand because most often they are different in value and definitely different in meaning. Whereas displacement takes the initial and final position into account, distance takes into account everywhere traveled between the initial and final position and does not distinguish directions.
A simple example that illustrates the difference between distance and displacement is a 50-meter race in a 25-meter swimming pool. See Figure 1 below. The distance of the race is 50 meters while the displacement is 0 meters. The displacement during the first half of the race is 25 meters and during the second half of the race is −25 meters. Note that displacement gives a sense of direction, while distance does not.
Overview
It is not clear when the concept of displacement was first used. However, Hooke’s Law, discovered in 1660, states that the displacement of a spring is directly proportional to the force being made on the spring. In this case, the displacement is the difference in the length of the spring and can be positive or negative.
In a single dimension, the displacement from x1 to x2 is denoted ∆x(x1, x2) and ∆x(x1, x2) = x2 – x1. Note that it is the final position minus the initial position. For this reason, the displacement from A to B is the opposite of the displacement from B to A. In two or three dimensions, displacement is specific to a direction. Consider Figure 2 below. Suppose an object followed the gray line shown between points A and B. The distance from A to B is 4 units. ∆x(A, B) = 4 – 1 = 3 and ∆y(A, B) = 2 – 1 = 1. The distance from B to A would also be 4 units. However, ∆x(B, A) = 1 – 4 = –3 and ∆y(B, A) = 1 – 2 = –1. The displacement values would be the same even if the object followed the path shown by the dotted curve.
Linear displacement is an important concept as it is used to define other values, often-used values such as average linear velocity, v = ∆x/∆t. Like displacement, average linear velocity can be positive or negative and is specific to the direction of the displacement. Angular movements also use displacement to describe the change in position of an object, as well as the corresponding average angular velocity. Strain, an important mechanical characteristics of materials, is the object’s displacement over its original length, or ∆ = ∆L/L. Mechanical work is defined as the product of the force made on the object and its displacement, W = F∆x.
Bibliography
Arfken, George B, and Hans J. Weber. Mathematical Methods for Physicists: A Comprehensive Guide. Burlington: Elsevier, 2012.
Hewitt, Paul G. Conceptual Physics. 12th ed. Upper Saddle River, NJ: Pearson, 2014.
Hsu, Tom. Physics: A First Course. 2nd edition. Nashua, NH: CPO, 2012.