Batterjee Medical College General Physics Chapter 2 Vectors 19-22 كلية البترجي الطبية فيزياء عامة

Chapter Two:
Vectors
Intended Learning Outcomes:
In this chapter we will
• Recognize vector quantities • Recognize vector properties
• Resolve vector into rectangular components • Recognize unit vectors
2.1 Vectors
2.1.1 Vectors and scalar quantities
Quantities in physics are divided to two major parts:
c) A scalar quantity: is completely specified by a single value with an appropriate unit and
has no direction. Like mass, time, temperature.
d) A vector quantity: is completely specified by a number and appropriate units plus a
direction. Like velocity, force, acceleration.
The length of the line shows its magnitude and the arrowhead points to the direction.
2.1.2 Some properties of vectors
1) Equality of two vectors. Two vectors 𝐴 ⃗ and 𝐵 ⃗⃗ are defined to be equal if they have the same magnitude and point in the same direction.
𝐴 ⃗ = 𝐵 ⃗⃗ Only if 𝐴 = 𝐵 and if A and B point in the same direction.
2) Adding vectors ** (Additional part)
When two or more vectors are added together all vectors involved must have the same units.
The rules for adding vectors are conveniently described by graphical methods. In geometric method:
a) Draw vector 𝐴 ⃗ with magnitude represented by a convenient length scale. b) Draw vector 𝐵 ⃗⃗ to the same scale, with its tail starting from tip of 𝐴 ⃗ . c) The resultant vector 𝑅 ⃗⃗ = 𝐴 ⃗ + 𝐵 ⃗⃗ is the vector drawn from the tail of 𝐴 ⃗ to
the tip of 𝐵 ⃗⃗ .
When two vectors are added, the sum is independent of the order of the addition.
𝐴 ⃗ + 𝐵 ⃗⃗ = 𝐵 ⃗⃗ + 𝐴 ⃗ Commutative law of addition. 𝐴 ⃗ + ( 𝐵 ⃗⃗ + 𝐶 ⃗ ) = (𝐴 ⃗ + 𝐵 ⃗⃗ ) + 𝐶 ⃗ Associative law of addition.
3) Negative of a vectors ** (Additional part) The negative of the vector 𝐴 ⃗ is defined as the vector that when added to 𝐴 ⃗ gives zero for the vector sum. That is, 𝐴 ⃗ + ( − 𝐴 ⃗ ) = 0. The vectors 𝐴 ⃗ and − 𝐴 ⃗ have the same magnitude but point in opposite directions.
4) Subtracting vectors ** (Additional part)
The operation of vector subtraction makes use the definition of the negative of a vector. We define the operation 𝐴 ⃗ − 𝐵 ⃗⃗ as vector − 𝐵 ⃗⃗ added to vector 𝐴 ⃗ :
𝐴 ⃗ − 𝐵 ⃗⃗ = 𝐴 ⃗ + ( − 𝐵 ⃗⃗ )
5) Multiplying a vector by a scalar ** (Additional part) If vector 𝐴 ⃗ multiply by a positive scalar quantity 𝑚, the product 𝑚 𝐴 ⃗ is a vector has the same direction of 𝐴 ⃗ and magnitude 𝑚𝐴.
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