TOPIC 2. Physical Quantities: Scalar and Vector Quantities. Lecture Outline. Scalar Quantities Vector Quantities Addition of Vector Quantities Application of Vector Quantities. Lecture Objectives. After this lecture, students will be able: To define scalar quantities
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Physical Quantities: Scalar and Vector Quantities
Scalar quantities are those which are described solely by their magnitudeSome examples are:
Mass e.g. 14 [kg], 36 [lbs], …
Time e.g. 10 seconds, 40 minutes, …
Volume e.g. 1000 cm3, 4 litres, 12 gallons
Temperature e.g 14 oF , 25 oC, …
Voltage e.g. 9 Volts, etc
Vector quantities are those which need to be described by BOTH magnitude and direction
Some of the most common examples which we will encounter are:
Velocity e.g. 100 [mi/hr] NORTH
Acceleration e.g. 10 [m/sec2] at 35o with respect to EAST
Force e.g. 980 [Newtons] straight down (270o)
Momentum e.g. 200 [kg m/sec] at 90o.
Arrange tail of vector B on tip of vector A. The vector sum C, called the resultant, is drawn from the tail of vector A to the tip of vector B. The order of addition does not matter.
C = A + B
Note: B has direction and size, but starting point is arbitrary
1. The negative of a vector is a vector of the same magnitude but in the opposite direction. Thus vector v = 5 m/s due east, then –v = 5 m/s due west.
2. In order to subtract one vector from another, rewrite the problem s that the rules of vector addition can be applied.
A – B can be written as A + (-B)
A vector R which lies at some angle q to an axis has two perpendicular components, Rxand Ry which lie on the axes.
If you draw a straight line from the tip of vector R to the axis, this distance along the axis is the magnitude of the component.
Applying trigonometry, the components of the vector R can be defined.
Rx = Rcos(q)
Ry = Rsin(q)
tan q = Ry / Rx
R = √(Rx2 + Ry2)