Two Dimensional Motion Unit 3.3 Vectors and Scalars Two Dimensional Motion Unit 3.3

Vectors and Scalars Previously we discussed motion in 2 directions, forwards and backwards, in a straight line. Now we are going to cover motion not in a straight line.

Physical quantities can be categorized as a scalar or vector. Vectors and Scalars Physical quantities can be categorized as a scalar or vector.

Vectors and Scalars A scalar is a quantity that can be completely specified by its magnitude with the appropriate units. Examples: speed - 125 km/hour volume - 450 mL

Vectors A vector is a quantity that has direction and magnitude. Examples: Velocity – 20 m/s South Displacement – 335 km East

Vectors Vectors are represented by symbols. Vectors can be written in italics [Y ] or in bold type [X]

Vectors If handwritten, a vector can be symbolized by showing an arrow drawn above the symbol. Z

Vectors One way to keep track of vectors and directions is to use diagrams.

Vectors Vectors can be added graphically. When adding vectors, you must make sure that they have the same units and describe similar quantities.

Vectors The addition of two or more vectors is called a resultant.

Vectors Vectors can be added graphically using a triangle method of addition, in which the tail of 1 vector is placed at the head of the other.

Vectors The resultant is the vector drawn from the tail of the first vector to the head of the last vector.

Vectors The resultant displacement can be found using a ruler and protractor.

Vectors

Vector or Scalar? Acceleration of a plane at take off Number of passengers on the plane Duration of the flight Displacement of the flight Amount of fuel of required for the flight

Vector or Scalar? Vector Scalar

Properties of Vectors Vectors can be moved parallel to themselves in a diagram. Vectors can be added in any order and the sum will remain the same as long as the magnitude and direction of each vector is the same.

Properties of Vectors To subtract a vector , add its opposite. The negative of a vector is defined as a vector with the same magnitude as the original vector but in the opposite direction.

Properties of Vectors Example: -35m x 3 = -105m Multiplying or dividing, vectors by scalars results in vectors. This is because vectors indicate direction which could be + or -. Example: -35m x 3 = -105m

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