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# UB PHY 107 - Significant Figures and Vectors

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PHY 107 1st Edition Lecture 2 Outline of Last Lecture I. MechanicsOutline of Current Lecture II. Significant FiguresIII. Vectors- Unit VectorsIV. Adding and subtracting vectorsCurrent LectureSignificant Figures (sig figs):- Depicts the level of accuracy in a measurement - The accuracy of the tool that you use is the accuracy that you must report your answer with  Ex. If you use a ruler with the smallest measurement being millimeters, you may report your answer as no more accurate than 1.234 m (4 sig figs) because the ruler cannot measure a fraction of a millimeter- ALL nonzero numbers are significant - When multiplying or dividing, the answer may have no more significant figures than the number with the least amount of sig figs that you are using Ex. 1 x 123.456 = 100 because the first term only has 1 significant figure- Leading zeros are not significant figures Ex. 0.00001 only has one significant figure- Any zero between 2 nonzero numbers is significant Ex. 1034 and 0.07009 both have 4 significant figures- If the number has a decimal point, all zeros to the right of the last nonzero number are significant  Ex. 0.01000 has 4 significant figures, the zeros after the 1 are significant Ex. 10000. has 5 significant figures, the zeros between the 1 and the decimal point are significant Vectors:These notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.- Vector – has magnitude and direction; denoted as a or ´a, magnitude denoted as a or |´a|  Ex. Displacement, velocity, acceleration- Scalar – has only magnitude, no direction  Ex. Temperature, mass- The vectors ´a and –´a have the same magnitude but opposite direction - When drawn in a coordinate plane with its tail centered at (0,0), every vector has x and y components which may be added together to get the original vector To find components:  X component, ax, use the equation: ax = acosθ Y component, ay, use the equation: ay = asinθ- Unit vectors – magnitude of 1 pointing in a particular direction (x, y, z axis) The unit vector centered at the origin pointed in the direction of the x axis is known as ´i The unit vector centered at the origin pointed in the direction of the y axis is known as ´j The unit vector centered at the origin pointed in the direction of the z axis is known as ´kAddition & Subtraction: - Addition is adding 2 vectors together to get a resultant vector, ´a+´b=´c- Subtraction is subtracting one vector from another to get a resultant vector,´a−´b= ´c- By negating one value, a subtraction problem can be turned into an addition problem: ´a−´b=´c→ ´a+(−´b)=´c- Graphically: Arrange the vectors “tip” to “tail” Draw a connecting line from the tail of the first to the tip of the last This line represents the resultant vector - Numerically (with components): Find the x and y components of each vector Add the x components of each vector and the y components of each vector to generate the x and y components of the resultant vector (subtract if necessary)´ab¿´¿c¿´¿´a+´b=´c To get the magnitude of the resultant vector, denoted |´a∨¿, use this equation:o |´a∨¿ = √ax2+ay2 To get the angle the resultant vector makes with the x-axis, use this equation:o tanθ =

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