Two-Dimensional Motion and Vectors Introduction to Vectors

Scalars and Vectors Every physical quantity can be described as a vector or a scalar Scalar – a physical quantity that has only magnitude, but no direction Speed, distance Vector – a physical quantity that has both magnitude and direction Velocity, displacement

Scalars and Vectors The book uses bold to represent vectors and italics to represent scalars Can also use directional arrows to denote vectors v

Vector Diagrams Use arrows to show direction Length of arrow shows relative strength of vector Long arrow has greater magnitude than short arrow

Vector Addition Can only add vectors with the same units and that describe similar quantities Cannot add displacement and velocity vectors Resultant – a vector representing the sum of two or more vectors

Triangle Method of Addition of Vectors Add vectors by drawing a to-scale diagram Measure the straight line distance from the tail of the initial vector to the head of the final vector Multiply by the scale Use a protractor to determine the direction of the resultant

Vector Addition Vectors can be moved parallel to themselves in a diagram Must remain pointing in the same direction Vectors can be added in any order Total displacement remains the same To subtract vectors – add the opposite A vector plus its opposite results in zero

Vector Addition

Vector Multiplication and Division Multiplying and dividing vectors by scalars results in vectors A cab driver is told to drive twice as fast Original velocity vcab is multiplied by scalar number 2 Result is 2vcab Twice as fast in opposite direction would be -2vcab