SCALAR QUANTITIES AND VECTOR QUANTITIES Sumber Gambar http://theworldoffii.blogspot.com/2008/07/alat-ukur-massa.html Sumber Gambar : site: gurumuda.files.wordpress.com SCALAR QUANTITIES AND VECTOR QUANTITIES

Scalar Scalar quantities is a value without a direction, such as: density, volume, temperature Length Time Energy page: 2 scalar

Scalar The scalar quantities comply with all rules of mathematical algebra Example: 1) Temperature: (300 K + 200 K) = 500 K 2) Power: 200 J + (-50 Joule ) = 150 Joule. page: 3 scalar

Vector Vector quantities is a value with a direction Example: displacement, velocity, acceleration, force Vector is expressed in a straight line with an arrow. The length of line shows the value of vector and the arrow direction shows the vector direction B AB b A vector AB vector b page: 4 vector

Vector Components Vector can be subdivided into 2 vector components, each of them has the same direction as X axis and Y axis in cartesian coordinate b b x y θ = b cos θ b sin θ page: 5 vector

ˆ ˆ ˆ Unit Vector Vector can be expressed as a unit vector b Unit Vector is a one unit vector and has the same direction with the vector component Vector can be expressed as a unit vector b b ˆ b = a Example 5 ˆ a = magnitude (value) b ˆ = unit vector page: 6 Unit vector

ˆ ˆ ˆ ˆ Unit Vector i = unit vector in the same direction as X axis j = unit vector in the same direction as Y axis y z x ˆ i k j k ˆ = unit vector in the same direction as Z axis Page: 7 unit vector

Unit Vector ˆ i ˆ j ˆ c = 4 + 5 + 8 k Vector can be expressed by unit vector as follows: c ˆ i ˆ j ˆ c = 4 + 5 + 8 k It means that vector has: 4 unit vector in the same direction as X axis, 5 unit vector in the same direction as Y axis, 8 unit vector in the same direction as Z axis c page: 8 unit vector

ˆ ˆ Unit Vector c = 4 + 5 + 8 i j k z 8 k 5 y 4 j i x page: 9 = 4 + 5 + 8 ˆ i j k y z x ˆ i k j 4 5 8 page: 9 unit vector

Addition of Vector Example: c b d = + b Vector can be result from 2 methods: d 1. Geometrical method 2. Analytical method c page: 10 addition of vector

Geometrical Method 1. Poligon b c b d c page: 11 Geometrical method

according cosinus rule: Geometrical Method 2. Paralellogram b c d θ b c according cosinus rule: page: 12 Geometrical method

Disruption of vector in cartesian coordinate Analytical Method Disruption of vector in cartesian coordinate b c x y α β bx cx cy by b c Page:13 analytical method

Disruption of vector in cartesian coordinate Analytical Method Disruption of vector in cartesian coordinate by = b sin α cy = c sin β b c x y α β bx cx cy by bx = b cos α cx = c cos β page: 14 analytical method

ˆ Analytical Method The direction of can be determined as : d d = dx + dy ˆ i j If  d dx dy dy = by + (-cy) dx = bx + cx The direction of can be determined as : d or page: 15 analytical method