COURSE WEBPAGES The Physics 218 Home webpage is located here: You can also find this syllabus, grades, course announcements, learning center hours and other important resources on the Blackboard webpage: We will use the Web Assign Computerized Homework system to assign credit for homework completed during the semester. The Web Assign webpage is: Web Assign HELP CENTER:

Nicholas J. Giordano Introduction

Isaac Newton Mechanics will be the first area studied Laws were developed by Sir Isaac Newton Laws of Motion Apply to a wide variety of objects Section 1.1

Can The Physical World Be Understood? Newton’s Answer: YES! Not only yes; The physical world is understandable in a limited number of simple statements Using these simple laws we can build an axiomatic system (like geometry) that gives us powerful insight and limited control of the world around us

Why Learn Physics? Many students state they can’t understand why they are forced to learn physics: There are two levels to the answer: (1) The study of the natural or material world and phenomena in order to understand how it works, so that we can be in harmony with it. (2) Gives and example of how to build an axiomatic system and work with such a system. Physics teaches us how to recognize the elements of such a system and apply such a system that may occur in a completely different context.

Dealing With Numbers Scientific notation Significant figures Recognizing them Using them in calculations Section 1.3

Scientific Notation Scientific notation is a useful way to write numbers that are very large or very small Scientific notation is necessary way to correctly write the significant figures in a number To write a number in scientific notation: Move the decimal point to create a new number with it’s first digit between 1 and 9 Count the number of places the decimal point was moved This is the exponent of 10 The exponent is positive if the original number is greater than one The exponent is negative if the original number is less than one Section 1.3

LQ-1 Write the speed of light in scientific notation C= 299,792,458 meters/second (a) 299,792,458 (b) x 10 5 (c) x 10 9 (d) x 10 8 (e) x 10 10

Significant Figures, Examples Example: 100 May have 1 significant figure Zeros are ambiguous Rewrite in scientific notation 1.00 x 10 2 shows 3 significant figures Example: significant figures In numbers less than 1, zeros immediately to the right of the decimal point are not significant Can also be clarified by writing in scientific notation: 1.23 x Section 1.3

Significant Figures in Calculations, cont. Addition and subtraction The location of the least significant digit in the answer is determined by the location of the least significant digit in the starting quantity that is known with the least accuracy Example: = 5.72 ~ 5.7 Due to the location of the significant digit in the 1.2 Section 1.3

Angle Measurements Units Degrees Radians 360° = 2 π rad Definition of radian s is the length of arc r is the radius s and r must be measured in the same units Section 1.7

Trigonometry Use right triangles Pythagorean Theorem r 2 = x 2 + y 2 Trig functions sin θ = y / r cos θ = x / r tan θ = y / x Trigonometric identities sin² θ + cos² θ = 1 Section 1.7

LQ-2 In terms of the angle alpha and R what is the project of R on the x-axis

Inverse Functions and Angles To find an angle use the inverse of a trig function If sin θ = y/r then θ = sin -1 (y/r) Angles in the triangle add up to 180° α + β + 90°= 180° Complementary angles sin α = cos β Section 1.7

Vectors vs. Scalars A scalar is a quantity that requires only a magnitude (with units) A vector is a quantity that requires a magnitude and a direction (with units) Often over looked! The Magnitude and Direction can be in an abstract space Section 1.8

Vectors Vectors may be Added Multiplied by a scalar Subtracted Resolved into components Section 1.8

Vector Representation The length of the arrow indicates the magnitude of the vector The direction of the arrow indicates the direction of the vector with respect to a given coordinate system Vectors are written with an arrow over a boldface letter Mathematical operations can be performed with vectors Section 1.8

Adding Vectors Draw the first vector Draw the second vector starting at the tip of the first vector Continue to draw vectors “tip-to-tail” The sum is drawn from the tail of the first vector to the tip of the last vector Example: Section 1.8

Multiplying Vectors by Scalars Multiplying a vector by a positive scalar only affects the vector’s magnitude It will have no effect on the vector’s direction Section 1.8

Subtracting Vectors To subtract a vector, you add its opposite Section 1.8

Components of Vectors The x- and y- components of a vector are its projections along the x- and y-axes Calculation of the x- and y-components involves trigonometry A x = A cos θ A y = A sin θ Section 1.8

Vector from Components If you know the components, you can find the vector Use the Pythagorean Theorem for the magnitude: Use the tan -1 to find the direction: Section 1.8

Adding Vectors Using Components Assume you are adding two vectors: To add the vectors, add their components C x = A x + B x C y = A y + B y Then the magnitude and direction of C can be determined Section 1.8