Resolution of Vectors Equilibrium of a Particle Overview When a set of forces act on an object in such a way that the lines of action of the forces pass through a common point‚ the forces are described as concurrent forces. When these forces lie in the same geometric plane‚ the forces are also described as coplanar forces. A single G G equivalent force known as the resultant force FR may replace a set of concurrent forces F1 and G F2 ‚ as shown. This resultant force is obtained by a process of vector addition
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"The Force Table" is a simple tool for demonstrating Newton’s First Law and the vector nature of forces. This tool is based on the principle of “equilibrium”. An object is said to be in equilibrium when there is no net force acting on it. An object with no net force acting on it has no acceleration. By using simple weights‚ pulleys and strings placed around a circular table‚ several forces can be applied to an object located in the center of the table in such a way that the forces exactly cancel
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HL Vectors Notes 1. Vector or Scalar Many physical quantities such as area‚ length‚ mass and temperature are completely described once the magnitude of the quantity is given. Such quantities are called “scalars.” Other quantities possess the properties of magnitude and direction. A quantity of this kind is called a “vector” quantity. Winds are usually described by giving their speed and direction; say 20 km/h north east. The wind speed and wind direction together form a vector quantity
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each of the following vectors in terms of and (a) (b) (c) (Total 4 marks) 2. The vectors ‚ are unit vectors along the x-axis and y-axis respectively. The vectors = – + and = 3 + 5 are given. (a) Find + 2 in terms of and . A vector has the same direction as + 2 ‚ and has a magnitude of 26. (b) Find in terms of and . (Total 4 marks) 3. The circle shown has centre O and radius 6. is the vector ‚ is the vector and is the vector . (a) Verify
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Acceleration Velocity Displacement Distance Time Definition 1. Acceleration is the rate of change of velocity with time. Velocity is a vector physical quantity; both magnitude and direction are required to define it. the length of an imaginary straight path‚ typically distinct from the path actually travelled by P. Distance is a numerical description of how far apart objects are. In physics or everyday usage‚ distance may refer to a physical length‚ or an estimation Time in physics is
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1.1.1 Show how to find A and B‚ given A+B and A −B. 1.1.2 The vector A whose magnitude is 1.732 units makes equal angles with the coordinate axes. Find Ax‚Ay ‚ and Az. 1.1.3 Calculate the components of a unit vector that lies in the xy-plane and makes equal angles with the positive directions of the x- and y-axes. 1.1.4 The velocity of sailboat A relative to sailboat B‚ vrel‚ is defined by the equation vrel = vA − vB‚ where vA is the velocity of A and vB is the velocity of B. Determine the velocity
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December 2011 Vectors Math is everywhere. No matter which way you look at it‚ it’s there. It is especially present in science. Most people don’t notice it‚ they have to look closer to find out what it is really made of. A component in math that is very prominent in science is the vector. What is a vector? A vector is a geometric object that has both a magnitude and a direction. A good example of a vector is wind. 30 MPH north. It has both magnitude‚(in this case speed) and direction. Vectors have specific
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a stochastic process with the following properties: (a.) The number of possible outcomes or states is finite. (b.) The outcome at any stage depends only on the outcome of the previous stage. (c.) The probabilities are constant over time. If x0 is a vector which represents the initial state of a system‚ then
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quantity which depends on direction a vector quantity‚ and a quantity which does not depend on direction is called a scalar quantity. Vector quantities have two characteristics‚ a magnitude and a direction. Scalar quantities have only a magnitude. When comparing two vector quantities of the same type‚ you have to compare both the magnitude and the direction. For scalars‚ you only have to compare the magnitude. When doing any mathematical operation on a vector quantity (like adding‚ subtracting‚ multiplying
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Vector Analysis Definition A vector in n dimension is any set of n-components that transforms in the same manner as a displacement when you change coordinates Displacement is the model for the behavior of all vectors Roughly speaking: A vector is a quantity with both direction as well as magnitude. On the contrary‚ a scalar has no direction and remains unchanged when one changes the coordinates. Notation: Bold face A‚ in handwriting A . The magnitude of the vector is denoted by A A
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