Physics 101: Lecture 3, Pg 1 Lecture 3: Introduction to Physics 101 Chapter 1 : Scalars and Vectors (1.5) Chapter 2: Distance and Displacement, Speed and Velocity (2.1,2.2)

Physics 101: Lecture 3, Pg 2 Conversion of Units – Example A Cheetah’s acceleration when hunting can be a=6.1 m/s 2 What is its acceleration in ft/min 2 ? Conversion factor: 1 ft = m ft/min ft/min x 10 3 ft/min 2 correct

Physics 101: Lecture 3, Pg 3 Dimensional Analysis - Example Determine how the time t of a free fall of an object depends on its mass m, the height h from which it is dropped and the acceleration g due to gravity. 1 - V h/g 2 - m h/g 3 - h/g correct

Physics 101: Lecture 3, Pg 4 Trigonometry - Example Which one of the following expressions may be used to correctly find the angle  ?  2 cm 5cm5cm 1 -  = cos -1 (5/2) 2 -  = tan -1 (2/5) 3 -  = tan -1 (5/2) correct 90

Physics 101: Lecture 3, Pg 5 Trigonometry Definition of sine, cosine and tangent: Right triangle: Sin  = h o /h Cos  = h a /h Tan  = h o /h a Pythagorean Theorem: h 2 = h o 2 + h a 2 Any Triangle: Laws of Cosines, Sines (see E.2)  hypotenuse h h o opposite to angle haha 90 adjacen t to angle

Physics 101: Lecture 3, Pg 6 Trigonometry - Example The silhouette of a Christmas tree is an isosceles triangle. The angle at the top of the triangle is 30 degrees, and the base measures 2 meters across. How tall is the tree (in meters) ?

Physics 101: Lecture 3, Pg 7 Scalars and Vectors Scalars are quantities which are completely specified by their magnitude (single number+unit). There are physical quantities which are not completely specified by their magnitude. Example: Displacement

Physics 101: Lecture 3, Pg 8 Scalars and Vectors Example: Displacement Displacement is the difference between final and initial position of a body. Assume a person is at an initial position A. What do you have to specify to completely pin down the person’s final position with respect to A ? To be able to describe both magnitude and direction of a physical quantity we use vectors.

Physics 101: Lecture 3, Pg 9 Vectors Vectors are graphically represented by arrows:  The direction of the physical quantity is given by the direction of the arrow.  The magnitude of the quantity is given by the length of the arrow.

Physics 101: Lecture 3, Pg 10 Addition and Subtraction of Vectors l Graphical: Tail-to-head method l Using vector components (e.g. 2 dimensional space) : R = A+B = (A x +B x ) x + (A y +B y ) y

Physics 101: Lecture 3, Pg 11 Lecture 3: Scalars and Vectors Distance and Displacement I strongly suggest that you try the example problems in the textbook. If you have trouble with any of them, please go to office hours for help!