File Name: scalar and vector quantities in physics .zip
This is a list of physical quantities.
Many familiar physical quantities can be specified completely by giving a single number and the appropriate unit. Scalar quantities that have the same physical units can be added or subtracted according to the usual rules of algebra for numbers. When we multiply a scalar quantity by a number, we obtain the same scalar quantity but with a larger or smaller value.
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 km in 1. Many physical quantities, however, cannot be described completely by just a single number of physical units. For example, when the U. Coast Guard dispatches a ship or a helicopter for a rescue mission, the rescue team must know not only the distance to the distress signal, but also the direction from which the signal is coming so they can get to its origin as quickly as possible.
Physical quantities specified completely by giving a number of units magnitude and a direction are called vector quantities. Examples of vector quantities include displacement, velocity, position, force, and torque. We can add or subtract two vectors, and we can multiply a vector by a scalar or by another vector, but we cannot divide by a vector. The operation of division by a vector is not defined. Analytical methods are more simple computationally and more accurate than graphical methods.
From now on, to distinguish between a vector and a scalar quantity, we adopt the common convention that a letter in bold type with an arrow above it denotes a vector, and a letter without an arrow denotes a scalar. For example, a distance of 2.
Suppose you tell a friend on a camping trip that you have discovered a terrific fishing hole 6 km from your tent. It is unlikely your friend would be able to find the hole easily unless you also communicate the direction in which it can be found with respect to your campsite. Displacement is a general term used to describe a change in position, such as during a trip from the tent to the fishing hole. Displacement is an example of a vector quantity. The arrowhead marks the end of the vector. Suppose your friend walks from the campsite at A to the fishing pond at B and then walks back: from the fishing pond at B to the campsite at A.
In Figure 2. Two vectors that have identical directions are said to be parallel vectors —meaning, they are parallel to each other. Two vectors with directions perpendicular to each other are said to be orthogonal vectors. Two motorboats named Alice and Bob are moving on a lake. Given the information about their velocity vectors in each of the following situations, indicate whether their velocity vectors are equal or otherwise. Vectors can be multiplied by scalars, added to other vectors, or subtracted from other vectors.
If he walks only a 0. All of this can be stated succinctly in the form of the following vector equation :. In a vector equation, both sides of the equation are vectors. In a scalar equation, both sides of the equation are numbers. Now suppose your fishing buddy departs from point A the campsite , walking in the direction to point B the fishing hole , but he realizes he lost his tackle box when he stopped to rest at point C located three-quarters of the distance between A and B, beginning from point A.
So, he turns back and retraces his steps in the direction toward the campsite and finds the box lying on the path at some point D only 1. The vector sum of two or more vectors is called the resultant vector or, for short, the resultant. The direction of the resultant is parallel to both vectors. In general, in one dimension—as well as in higher dimensions, such as in a plane or in space—we can add any number of vectors and we can do so in any order because the addition of vectors is commutative ,.
When adding many vectors in one dimension, it is convenient to use the concept of a unit vector. The only role of a unit vector is to specify direction. In this way, the displacement of 6. Samuel J. Learning Objectives Describe the difference between vector and scalar quantities.
Identify the magnitude and direction of a vector. Explain the effect of multiplying a vector quantity by a scalar. Describe how one-dimensional vector quantities are added or subtracted. Explain the geometric construction for the addition or subtraction of vectors in a plane. Distinguish between a vector equation and a scalar equation.
Exercise 2. Alice moves north at 6 knots and Bob moves west at 6 knots. Alice moves west at 6 knots and Bob moves west at 3 knots. Alice moves northeast at 6 knots and Bob moves south at 3 knots. Alice moves northeast at 6 knots and Bob moves southwest at 6 knots. Alice moves northeast at 2 knots and Bob moves closer to the shore northeast at 2 knots. Algebra of Vectors in One Dimension Vectors can be multiplied by scalars, added to other vectors, or subtracted from other vectors.
Contributors and Attributions Samuel J.
The difference between a scalar and a vector is that a vector requires a direction. Scalar quantities have only magnitude; vector quantities have both magnitude and direction. Time is completely separated from direction; it is a scalar. It has only magnitude, no direction. A vector has both magnitude and direction, while a scalar has only magnitude. Ask yourself, "for which of these things is there a direction?
Scalar quantities are completely described by magnitude only (temperature ). Vector quantities need both magnitude (size) and direction to completely describe.
Vector , in physics , a quantity that has both magnitude and direction. Although a vector has magnitude and direction, it does not have position. That is, as long as its length is not changed, a vector is not altered if it is displaced parallel to itself.
Physics is a mathematical science. The underlying concepts and principles have a mathematical basis. Throughout the course of our study of physics, we will encounter a variety of concepts that have a mathematical basis associated with them. While our emphasis will often be upon the conceptual nature of physics, we will give considerable and persistent attention to its mathematical aspect. The motion of objects can be described by words. Even a person without a background in physics has a collection of words that can be used to describe moving objects. Words and phrases such as going fast , stopped , slowing down , speeding up , and turning provide a sufficient vocabulary for describing the motion of objects.
To better understand the science of propulsion it is necessary to use some mathematical ideas from vector analysis. Most people are introduced to vectors in high school or college, but for the elementary and middle school students, or the mathematically-challenged:. There are many complex parts to vector analysis and we aren't going there. We are going to limit ourselves to the very basics.
Many familiar physical quantities can be specified completely by giving a single number and the appropriate unit. Scalar quantities that have the same physical units can be added or subtracted according to the usual rules of algebra for numbers. When we multiply a scalar quantity by a number, we obtain the same scalar quantity but with a larger or smaller value. 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 km in 1. Many physical quantities, however, cannot be described completely by just a single number of physical units.
Scalars and scalar quantities. Vectors and vector quantities. Representing scalars and vectors. 3 Introducing vector algebra. Scaling vectors.
In the study of physics, there are many different aspects to measure and many types of measurement tools. Scalar and vector quantities are two of these types of measurement tools. Keep reading for examples of scalar quantity and examples of vector quantity in physics. Understanding the difference between scalar and vector quantities is an important first step in physics. The main difference in their definitions is:. In other words, scalar quantity has magnitude, such as size or length, but no particular direction. When it does have a particular direction, it's a vector quantity.
Direction is symbolized by. The reference point is usually. If you begin a trip from home, then home is your reference point. Specifying where you are or where you are going requires you to indicate the direction. In writing,.
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VECTOR QUANTITIES IN. MECHANICS AND MOTION. ANALYSIS. CHAPTER objectives. To give students a good basic understanding of vectors and scalars.Ittmar N. 24.05.2021 at 03:15
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