Theory of equations by James Victor Uspensky

By James Victor Uspensky

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To find the magnitude of the new vector, B, simply multiply the magnitude of A by |n|, the absolute value of n. To determine the direction of the vector B, we must look at the sign on n. If n is a positive number, then B and A are in the same direction. However, if n is a negative number, then B and A point in opposite directions. For example, if vector A is multiplied by the scalar +3, then the new vector B is three times as long as A, and points in the same direction. If vector A is multiplied by the scalar –3, then B would still be three times as long as A but would now point in the opposite direction.

Mass (m) is a measure of a body’s inertia—the amount of matter in the object. Mass is a scalar quantity, and, as such, has magnitude only. The SI unit for mass is the kilogram, which is independent of gravity. One kilogram of material on Earth will have the same mass as one kilogram of material on the Moon. Weight ( Fg), on the other hand, is a measure of gravitational force (usually that of the Earth) on an object’s mass. Because weight is a force, it is a vector quantity with the units of newtons (N).

1: Before you move on, assess your understanding of the material with these questions. If the newton is the product of kilograms and meters/second2, what units comprise the pound? Order the following units from smallest to largest: centimeter, angstrom, inch, mile, foot. 2 Vectors and Scalars Vectors are numbers that have magnitude and direction. Vector quantities include displacement, velocity, acceleration, and force. Scalars are numbers that have magnitude only and no direction. Scalar quantities include distance, speed, energy, pressure, and mass.

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