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# Physics and Displacement Help

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By McGraw-Hill Professional
Updated on Sep 4, 2011

## Introduction to Displacement

Displacement is also known as distance . Unless otherwise specified, displacement is defined along a straight line. We might say that Minneapolis, Minnesota, is 100 km from Rochester, Minnesota, “as the crow flies,” or along a straight line. If you were to drive along U.S. Route 52, however, the displacement would turn out to be closer to 120 km because this highway does not follow a straight path from Rochester to Minneapolis.

## Displacement As A Vector

When displacement is defined in a straight line, it is a vector quantity because it has both magnitude (expressed in meters, kilometers, or other distance units) and direction (which can be defined in various ways). Displacement magnitude is denoted by a lowercase italicized letter; let’s call it q . A displacement vector is denoted by a lowercase boldface letter. In this discussion, let’s use q .

The displacement vector q rm of Minneapolis relative to Rochester would be approximately 100 km in a northwesterly direction “as the crow flies.” As an azimuth bearing, it would be around 320 degrees, measured clockwise from true north. However, if we speak about driving along Route 52, we can no longer define the displacement as a vector because the direction changes as the road bends, goes over hills, and dips into valleys. In this case, we must denote displacement as a scalar, usually in lowercase italics. In this discussion let’s use q . We write q rm ≈ 120 km.

## How Displacement Is Determined

Displacement magnitude is determined by mechanically measuring distance or by inferring it with observations and mathematical calculations. In the case of a car or truck driving along Route 52, displacement is measured with an odometer that counts the number of wheel rotations and multiplies this by the circumference of the wheel. In a laboratory environment, displacement magnitude can be measured with a meter stick , by triangulation , or by measuring the time it takes for a ray of light to travel between two points given the constancy of the speed of light ( c ≈ 2.99792 × 10 8 m/s).

The direction component of a displacement vector is determined by measuring one or more angles or coordinates relative to a reference axis. In the case of a local region on the Earth’s surface, direction can be found by specifying the azimuth , which is the angle clockwise relative to true north. This is the scheme used by hikers and backpackers. In three-dimensional space, direction angles are used. A reference axis, for example, a vector pointing toward Polaris, the North Star, is defined. Then two angles are specified in a coordinate system based on this axis. The most common system used by astronomers and space scientists involves angles called celestial latitude and celestial longitude or, alternatively, right ascension and declination . Both these schemes are defined in Chapter 3. (If this is not familiar to you, and if you didn’t see fit to study Part Zero, this might be a good time to reconsider that decision!)

Practice problems of these concepts can be found at: Mass, Force, And Motion Practice Test

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