Introduction and Mathematical Concepts

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Presentation transcript:

Introduction and Mathematical Concepts Chapter 1 Introduction and Mathematical Concepts

1.4 Trigonometry

1.4 Trigonometry

1.4 Trigonometry

1.4 Trigonometry

1.4 Trigonometry

1.4 Trigonometry Pythagorean theorem:

A scalar quantity is one that can be described by a single number: 1.5 Scalars and Vectors A scalar quantity is one that can be described by a single number: temperature, speed, mass A vector quantity deals inherently with both magnitude and direction: velocity, force, displacement

By convention, the length of a vector 1.5 Scalars and Vectors Arrows are used to represent vectors. The direction of the arrow gives the direction of the vector. By convention, the length of a vector arrow is proportional to the magnitude of the vector. 8 lb 4 lb

1.5 Scalars and Vectors

1.6 Vector Addition and Subtraction Often it is necessary to add one vector to another.

1.6 Vector Addition and Subtraction 3 m 5 m 8 m

1.6 Vector Addition and Subtraction

1.6 Vector Addition and Subtraction 2.00 m 6.00 m

1.6 Vector Addition and Subtraction 2.00 m 6.00 m

1.6 Vector Addition and Subtraction 6.32 m 2.00 m 6.00 m

1.6 Vector Addition and Subtraction When a vector is multiplied by -1, the magnitude of the vector remains the same, but the direction of the vector is reversed.

1.6 Vector Addition and Subtraction

1.7 The Components of a Vector

1.7 The Components of a Vector

1.7 The Components of a Vector It is often easier to work with the scalar components rather than the vector components.

1.7 The Components of a Vector Example A displacement vector has a magnitude of 175 m and points at an angle of 50.0 degrees relative to the x axis. Find the x and y components of this vector.

1.8 Addition of Vectors by Means of Components

1.8 Addition of Vectors by Means of Components