VECTOR MECHANICS Rules for Graphical Vector Addition Ms

Introduction o In this chapter you will n n n Study the effects of

2. 2 Forces in a Plane o Forces on a Particle: the action of

2. 2 Forces in a Plane o Magnitude n Characterized by a certain number

2. 2 Forces in a Plane o Infinite straight line = line of action

2. 2 Forces in a Plane o Resultant n Two forces acting on a

2. 4 Vectors o Vectors n n n Mathematical expressions possessing magnitude and direction

2. 4 Vectors o Scalar n Physical quantities that do not have direction o

2. 4 Vectors o Represented by arrows n n n o In text by

2. 4 Vectors o Fixed Vectors (Bound) n Well-defined point of application o o

2. 3 Vectors o Equal vectors have same magnitude and direction P P

2. 3 Vectors o Negative vector of a given vector P is defined as

2. 4 Addition of Vectors o P+Q=Q+P o Addition of Vectors is Commutative o

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VECTOR MECHANICS Rules for Graphical Vector Addition Ms. Peace

Introduction o In this chapter you will n n n Study the effects of forces acting on a particle Learn how to replace two or more forces acting on a particle by a single force having the same effect Resultant Develop the relations which exist among the various forces acting on a particle in equilibrium

2. 2 Forces in a Plane o Forces on a Particle: the action of one body on another n Characterized by o o o n Point of Application Magnitude Direction Forces on a given particle have the same point of application so we will completely define by magnitude and direction

2. 2 Forces in a Plane o Magnitude n Characterized by a certain number of units o o o N newton k. N kilonewton lb pound kip kilopound Direction n Defined by the line of action and the sense of the force

2. 2 Forces in a Plane o Infinite straight line = line of action 10 lb A 30°

2. 2 Forces in a Plane o Resultant n Two forces acting on a particle can be replaced by a single force P R A Q

2. 4 Vectors o Vectors n n n Mathematical expressions possessing magnitude and direction and add according to the parallelogram law and triangle law Displacements Velocities Accelerations Momenta

2. 4 Vectors o Scalar n Physical quantities that do not have direction o o o Volume Mass Energy

2. 4 Vectors o Represented by arrows n n n o In text by boldface Letter with an arrow above it Underlined letter Magnitude of a vector n Defines the length of a vector used to represent it

2. 4 Vectors o Fixed Vectors (Bound) n Well-defined point of application o o Free Vectors n Freely moved in space o o The particle itself Couples Sliding Vectors n Forces acting on a rigid body slid along line of action

2. 3 Vectors o Equal vectors have same magnitude and direction P P

2. 3 Vectors o Negative vector of a given vector P is defined as a vector having same magnitude as P and direction opposite to that of P P -P P + (-P) = 0 equal and opposite vectors

2. 4 Addition of Vectors o P+Q=Q+P o Addition of Vectors is Commutative o Laws/Rules to find resultant graphically n n n Parallelogram Law Polygon Method/ Triangle Law Component Method