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# Physics with Calculus, Week 1&2 notes PH 211 - T12

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This 27 page Study Guide was uploaded by Parker Moore on Thursday October 6, 2016. The Study Guide belongs to PH 211 - T12 at Portland State University taught by Jonathan J Abramson (P) in Fall 2016. Since its upload, it has received 224 views. For similar materials see GEN PHYSICS W/CALCULUS in PHYSICS (PHY) at Portland State University.

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Date Created: 10/06/16

Physics 211/221 Week 2 PSU: Fall term Chapter 3: Vector- has a magnitude (length) as well as a direction Example of a vector Vector Broken up into x & y coordinates Scalar- temperature, pressure, energy, mass and time are examples of “scalars” that do not point in a direction Subtracting Vectors Adding Vectors Note: A+B=C Component – projection of the vector on an axis (if we have a vector called vector A then the components would be Ax & Ay in a 2D plane) Resolving the Vector – process of finding the components of a vector If given the length and angle use the formula below to find components *Vector A’s length(magnitude) is 12 and angel is 20° *Ignore the Bx & By If given components use formula below to find length and angle *V1 & V2 are components similar to Vx & Vy respectively *TIP: Read sample problem on page 44-45 in textbook, go slow and take in information one step at a time Adding vectors by components- * F1x + F2x = Rx * F1y + F2y = Ry *TIP: Read sample problem on page 48-49 in textbook Dot Product (a.k.a. scalar product) *Note: In the equation above the bold V * W are vectors while the lighter V W are the lengths (magnitude) of the vectors. Cross product- product of two vectors *Note: The magnitude(length) of the new vector (in this case ‘C’) is c = ab sin(theta) *Where a & b are the magnitudes(length) of vectors A and B *TIP: Read sample problem on page 54-55 in textbook In Class Notes – **NOTE: This is the same information as above but my own personal notes taken in class Resource page: These are links I found useful outside of the textbook and in class notes. Here is a link to solutions to the homework problems: http://www.slader.com/textbook/9781118230718-fundamentals-of-physics-10th- edition/10/problems/23/ Youtube: *If you need further explanation or some visual examples link a provided link Vectors & Scalars - https://www.youtube.com/watch?v=ihNZlp7iUHE Adding & Subtracting Vectors - https://www.youtube.com/watch?v=5Zfe4kfcZio Components of Vectors - https://www.youtube.com/watch?v=6Kw2nIwWYL0 Dot product of Vectors - https://www.youtube.com/watch?v=4hIh8ujylWE Cross product of Vectors - https://www.youtube.com/watch?v=qsgK1d-_8ik Chapter 4: Position Vector – vector that extends from a reference point (usually the origin) to the particle Vector Displacement- *TIP: Read sample problem on page 63-64 in textbook on Position and Displacement The r in the equation below is equal to displacement. T stands for time. *TIP: Read sample problem on page 67 in textbook on average/instantaneous velocity Average acceleration = change in velocity/change in time *TIP: Read sample problem on page 69 in textbook on average/instantaneous velocity Projectile- a projected or launched object Projectile motion- form of motion in which an object or particle is thrown near the earth’s surface, and it moves along a curved path under the action of gravity only Example 1- Example 2- *TIP: Read page 71-75 in textbook on projectile motion (trust me you’ll thank me later) Uniform circular motion- motion of an object in a circle at a constant speed. As an object moves in a circle, it is constantly changing its direction. At all instances, the object is moving tangent to the circle Centripetal acceleration – Consider an object moving in a circle of radius r with constant angular velocity. The tangential speed is constant, but the direction of the tangential velocity vector changes as the object rotates. *Can also be written as T=2π/v *TIP: Read sample problem on page 77 in textbook on circular motion Relative Motion- *TIP: Read sample problem on page 79 in textbook on circular motion Relative motion in two dimensions- *TIP: Read sample problem on page 80-81 in textbook on circular motion Resources Page: *TIP: I highly recommend reading page 81-82 which is a summary of the chapter to gain a better understanding *TIP: Make sure to do any and all homework problems assigned. Use these notes as well as the sample problems you read through to complete assigned homework. Solutions to the homework can be found here- http://www.slader.com/textbook/9781118230718-fundamentals-of-physics-10th- edition/10/problems/23/ Position Vector Examples/Solutions - http://www.onlinemathlearning.com/position-vector.html Youtube: Vector Acceleration/Velocity - https://www.youtube.com/watch?v=0iihgvZ7bVg Uniform circular motion - https://www.youtube.com/watch?v=sBFgRQuiqSM Relative motion in two dimensions - https://www.youtube.com/watch?v=gxDljxG9Ca0 Relative Velocity - https://www.youtube.com/watch?v=prhUQGgX8oU Physics 211/221 Week1 Fall 2016 These are my notes for week1. This should be used as a tool to quickly access valuable information pertaining to the class. It is best paired with looking at the example problems within the chapters as well as reviewing the homework problems (practice makes perfect). I have included the solutions to all homework problems in a link at the end of these notes. Chp.1 Quantity unity chart: Prefixes for SI units: The prefixes do not include the standard unit of a meter, second, gram ect. However they are all based around these standard units, for instance a deci-meter is 0.01meters Significant figures: When working out a problem always be consistent with the digits you use. For example if all the number in your problem end in the hundredth place (1.02) then your answer must also round to the hundredth place. Sig Figs are about maintaining accuracy throughout the problem. Also don’t confuse decimals with sig figs. 75.2m, 7.52m and 0.0075m all have three significant figures. Meter – length of the path traveled by light in a vacuum during a time interval of 1/299,792,458 of a second Second: one second is the time taken by 9,192,631,770 oscillations of the light (of a specified wavelength) emitted by a cesium-133 atom. 1 atomic mass unit (u) = 1.660 538 86 * 10^-27 kilograms (kg) Formula for Density: Density(p) = Mass (m) / Volume(V) p= m/V These equations will help with homework problem 1-1: These equations will help you with problem 1-9: Chp. 2 Signs. A plus sign for displacement need not be shown, but a minus sign must always be shown. If we ignore the sign of a displacement, we are left with the magnitude (or absolute value) of the displacement. For example a change in position to -4m (4 meters to the left) would have a magnitude of 4 m. *TIP: Read page #17 in textbook to get a walkthrough of an example problem Instantaneous velocity: is how fast a particle is moving at a given instant. Note: If the signs of the velocity and acceleration of a particle are the same, the speed of the particle increases. If the signs are opposite, the speed decreases. Note: Free fall acceleration is equal to -9.8m/s^2 **Best way to learn is to read through these example problems!!** *TIP: Read page #22 in textbook for a walkthrough example problem *TIP: Read page #24 in textbook for a walkthrough example problem *TIP: Read page #28 in textbook for a walkthrough example problem *TIP: Read page #30 in textbook for a walkthrough example problem Zoom in on photos below for better viewing. (Ctrl + scroll up) Resource page: These are links I found useful outside of the textbook and in class notes. Here is a link to solutions to the homework problems: http://www.slader.com/textbook/9781118230718-fundamentals-of-physics-10th- edition/10/problems/23/ *TIP: If you cannot understand one of the problems try googling the question. If this doesn’t work e-mail one of the assistant teachers for help. *TIP: Click the links below relating to the topic you need help on, if you need help on all click in order This is a link that’ll refresh your memory on Calculus integrals https://www.mathsisfun.com/calculus/integration-introduction.html This link will give you a better understanding of the linear motion formulas http://www.engineeringtoolbox.com/motion-formulas-d_941.html Here is a link to instantaneous velocity/average velocity examples(*THIS IS A VALUABLE LINK*) http://www.themathpage.com/acalc/instantaneous-velocity.htm YOUTUBE: Link to video explaining linear motion/formulas https://www.youtube.com/watch?v=fScAQvnq30M Alternative video explaining similar concepts https://www.youtube.com/watch?v=wQupPFO0P8M

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