AP1200_Ch1_Mechanics-2007 - AP1200 Foundation Physics...

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AP1200 Foundation Physics Limited wisdom and incorrect predictions: “Heavier-than-air flying machines are impossible.” -- Lord Kelvin, President, Royal Society, London, 1895. "Airplanes are interesting toys but of no military value." -- Maréchal Ferdinand Foch, Professor of Strategy, France. “Professor Goddard does not know the relation between action and reaction and the need to have something better than a vacuum against which to react. He seems to lack the basic knowledge taught daily in high schools.” -- 1921 New York Times editorial about Robert Goddard's revolutionary rocket work. "Drill for oil? You mean drill into the ground to try and find oil? You're crazy." -- Drillers who Edwin L. Drake asked to help him drill for oil in 1859. "If I had thought about it, I wouldn't have done the experiment. The literature was full of examples that said you can't do this." -- Spencer Silver on the work that led to the unique adhesives for 3-M "Post-it" notepads. Chapter 1: Mechanics z Velocity and acceleration z Newton’s laws of motion z Forces & torques z Kinetic and potential energy z Linear motion z Gravitational forces 1.1 Vectors Vectors are commonly used in Physics and will be introduced in this course. 1.1.1 Definitions A vector quantity is a quantity that has both a magnitude and a direction . In contrast, a scalar quantity has magnitude only and no direction. Some examples: Vectors Scalars Displacement Distance Velocity Speed Acceleration mass Force Time 1
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To distinguish vectors from scalars, we use the notations (in one dimension, we often use a for a vector, for convenience, but a can then have a negative or positive sign, i.e. a direction): Vector = a , a or a r Scalar = a Vectors are combined according to their own set of rules, see Fig. 1.1: vector addition . Fig. 1.1 Displacement An object may travel along the red curved line, but we can express the displacement, i.e. the position of B relative to A as a vector, a r . B is a certain distance and direction from A. Similarly, vector b r represents the displacement of position C relative to B. The displacement of C relative to A, , can be found by adding the vectors: s r b a s v v r + = 1.1.2 Components of a Vector If a vector is placed in a rectangular coordinate system with coordinate axes x and y (Fig. 1.2), it can be expressed in terms of its components along those axes: θ cos a a x = and sin a a y = (1.1) Fig. 1.2 Components of a vector The magnitude of the vector is a r 2 2 y x a a a + = r , hence in polar form with Cartesian (i.e. perpendicular) coordinate axes we can write: 2 2 y x a a a + = and x y a a = tan (1.2) The properties of a vector and relations among vectors, as well as the relations of physics, do not depend on the choice of coordinate system. Therefore the laws of physics are very frequently presented in vector form.
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This note was uploaded on 01/11/2011 for the course AP 1200 taught by Professor Michela.vanhove during the Spring '10 term at City University of Hong Kong.

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AP1200_Ch1_Mechanics-2007 - AP1200 Foundation Physics...

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