BarCharts QuickStudy Academic. Physics 2007

Textbook in PDF format Scalar and Vector Quantities. Physical quan tities such as temperature, T, distance, s, density, p, work, W, etc., that can be fully described by a single number are called scalars. Scalars are not associ ated with any direction. Physi cal quantities that have both magnitude and direction are called vectors, e.g, force, F, ve locity, V, acceleration, a, mo mentum, P, etc. • Coordinate Systems. A vector, V, can be described in reference to a coordinate sys tem. Two-dimensional coordi nate systems can be cartesian or polar. Three-dimensional coor dinate systems can be cartesian, cylindrical or spherical. DIMENSIONAL (3-D) COORDINATE SYSTEMS: Cartesian Coordinates (x,y,z) A vector, V, in a 3-D cartesian coordinate system can be written as: 4 v2+v2+v7v=¥.(vx,Vy,vz)=vxi+Vyi+vzk 3-D Cartesian Coordinates VECTOR ALGEBRA • Vector Addition. The sum of two coordinate system is a vector, VR, defined as: V =v +v —R-La In component notation, the summa tion is given as: VRX = VAX + VBX > VR\ =K\V + VBY Vector Addition yl yB VAx Vbx Right-Handed Rule v xV -B -A VAxVB=-V„xVA A cartesian coordinate system is called a right-handed system if i xj = k. If two vectors are parallel to each then: v v -B ’ Z-A |1 —B If the vectors are given in terms of their components, then in a 3-D

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