Science Basics and Introduction to Kinematics Physics Science Basics and Introduction to Kinematics

Things you should already know… Significant figures basics (always estimate 1 digit) Metric System and the Metric Prefixes The Greek alphabet This information will not be “covered” in class, however, it will come up almost every day. You are responsible for knowing this information.

Introduction to Kinematics Mechanics  the study of the motion of objects. Motion  the change in position and/or orientation of an object. All motion is relative  that is all objects move w/r/t (with respect to) other objects.  in order to describe the motion of an object it must be compared to another object. Question: Are you moving? Answer: You could answer yes or no and be correct depending on your frame of reference. For example, you could say, “compared to my desk…I am not moving.” Or you could say, “compared to the sun…I am moving.”

So, how do we describe motion? Kinematics The study of HOW things move. This encompasses things like speed, velocity and acceleration. Dynamics The study of WHY things move. This encompasses things like forces and energy.

Distance v. Displacement (d, s, r) A scalar quantity describing the total path length. Think about: “how far did you actually travel?” miles added to the odometer of your car. Displacement (x, y, d, D, s, r) A vector quantity describing the straight line distance between two points. Think about: “Where are you from where you started?” - How far ? - In what direction?

What the heck are scalar and a vector quantities? Scalars Quantities that have (only) a magnitude* associated with it. Examples Distance (20 miles) Speed (5 mph) Time (30 seconds) Mass (12 kg) *magnitude = size/number Vectors Quantities that have a magnitude AND a direction. Examples Displacement (20 miles EAST) Velocity (5 mph EAST) Acceleration (10 m/s2 EAST) Force (20 pounds LEFT)

So… back to Distance vs. Displacement The red line below shows the path that you drive. Your DISTANCE traveled is 8 miles (your odometer goes up by 8 miles The green line below shows your displacement. Notice that it is shorter than the distance and has a direction associated with it (from start to stop indicated by the arrow head. start stop

Speed and Velocity Speed (denoted as v or s): is the (time) rate at which you travel a given distance. Because speed is defined using a scalar quantity (distance) it is also a scalar quantity. Average speed (denoted as or ) is the rate at which a total distance is covered in a (total) time period. It is perfectly acceptable and common to drop the sigma notation. BOTH can be used to represent speed This is the Greek letter “Sigma”. Sigma means “SUM,” so this indicates that you need to have the TOTAL DISTANCE traveled and the TOTAL TIME spent.

You can use x or d to denote displacement. Speed and Velocity Velocity (denoted as v): is the (time) rate at which you travel a given displacement. It is the rate at which your position changes. Because velocity is defined using a vector quantity (displacement), it is also a vector quantity. Because it is a vector it will indicate how fast AND in what direction. Average velocity (denoted as ) is the rate at which a displacement is covered in a (total) time period. You can use x or d to denote displacement. This is a personal preference. Just make sure that YOU KNOW what you are representing. Average velocity

Wait a second… check this out …it might help. Speed and Velocity So, we said that you could represent speed in the following way…. If you drop the sigma notation you have…. This would mean that , average speed equals the (total) distance over the (total) time. Notice that this is the same notation as we had for average velocity. YES…the equation is the same for speed and velocity. If this blows your mind…and is too much for you to handle…you may want to drop physics now! What…? Really…? Wait a second… check this out …it might help. YOU HAVE TO KNOW WHAT THE CONTEXT OF THE PROBLEM IS IN ORDER TO KNOW WHEN TO USE THIS FOR SPEED AND WHEN TO USE THIS FOR VELOCITY.

Speed and Velocity We also like to represent quantities graphically…. Consider a graph in which position is plotted on the y-axis and time is on the x-axis as shown below. Consider the change that is occurring from 0-2 seconds. Time (s) Position (feet) 2 4 6 8 10 8 6 4 2 -2 -4 The time is easy…. time frame = ∆t = 2 sec The change in position can be expressed in two ways: Distance traveled =∆d = 2ft (you physically walked 2 feet) Displacement from starting point = ∆D +2ft (you are 2 feet (in the positive direction) away from where you started)

Speed and Velocity Position (feet) The time frame = ∆t = 2 sec Time (s) Position (feet) 2 4 6 8 10 8 6 4 2 -2 -4 The time frame = ∆t = 2 sec The change in position can be expressed in two ways: Distance traveled =∆d = 2m Displacement from starting point = ∆D +2m

Speed and Velocity The time frame = ∆t = 2 sec = ∆x Position (feet) Time (s) Position (feet) 2 4 6 8 10 8 6 4 2 -2 -4 The time frame = ∆t = 2 sec = ∆x The change in position can be expressed in two ways: Distance traveled =∆d = 2ft =∆y Displacement from starting point = ∆D +2ft =∆y Average speed = Average velocity =

Speed and Velocity You used ∆y/∆x = slope NOTICE for BOTH Average speed = NOTICE for BOTH You used ∆y/∆x = slope Average velocity =

Speed and Velocity You used ∆y/∆x = slope NOTICE for BOTH Average speed = NOTICE for BOTH You used ∆y/∆x = slope Average velocity =

Speed and Velocity To find the average speed OR average velocity from a position-v-time graph you need to use slope: ∆y/∆x = slope ∆d/∆t = v You used ∆y/∆x = slope

…this is NOT always the case! (We’ll explore this in class.) Speed and Velocity You used ∆y/∆x = slope CAUTION! In this example, the average speed and average velocity were the same magnitude (number)… …this is NOT always the case! (We’ll explore this in class.)

Remember…. It is your responsibility to have the notes presented in this PowerPoint written in your own writing (by the due date*).

Remember…. "I learned very early the difference between knowing the name of something and knowing something." — Richard P. Feynman It is NOT enough that you just copy down this information…or that you know a definition…you need to UNDERSTAND the definitions, how to apply them and when to apply them.