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0.1: Introduction to Scalars

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Mechanical Engineering

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Introduction to Scalars

0.1: Introduction to Scalars

Many familiar physical quantities can be specified completely by giving a single number and the appropriate unit. For example, "a class period lasts 50 min," or "the gas tank in my car holds 65 L," or "the distance between the two posts is 100 m." A physical quantity that can be specified completely in this manner is called a scalar quantity. The word "scalar" is a synonym for "number." Time, mass, distance, length, volume, temperature, and energy are some examples of scalar quantities.

Scalar quantities that have the same physical units can be added or subtracted according to the usual rules of algebra for numbers. For example, a class ending 10 min earlier than 50 min lasts 50 min − 10 min = 40 min. Similarly, a 60 cal serving of corn followed by a 200 cal serving of donuts gives 60 cal + 200 cal = 260 cal of energy. When we multiply a scalar quantity by a number, we obtain the same scalar quantity but with a larger (or smaller) value. For example, if yesterday's breakfast had 200 cal of energy and today's breakfast has four times as much energy as yesterday, then today's breakfast has 4 × 200 cal = 800 cal of energy. Two scalar quantities can also be multiplied or divided by each other to form a derived scalar quantity. For example, if a train covers a distance of 120 km in 1 h, its speed is 120,000 m/3600 s = 33 m/s, where the speed is a derived scalar quantity obtained by dividing distance with time.

This text is adapted from Openstax, University Physics Volume 1, Section 2.1: Scalars and Vectors.


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