Physics 121: Fundamentals of Physics I

Physics 121:Fundamentals of Physics I September 8, 2006 University of Maryland

Announcements / Reminders • Next homework is available on WebAssign • Free WebAssign use expires next Wednesday! • Tutorials (Discussion Sections) and Labs will begin meeting next week University of Maryland

Outline • Example Dimensional Analysis Problem • Describing Motion: • Coordinates in space and time • The idea of velocity • average velocity • instantaneous velocity • graphing velocity University of Maryland

Dimensional Analysis • In the following equation, determine what the dimensions of g have to be in order for the equation to be physically meaningful: • where [v]=L/T, [x]=L and [m]=M • L is length • M is mass • T is time University of Maryland

Describing Motion: Space • Coordinates — telling where something is • What do we need to do to specify the location of something so someone else can find it? • Note the difference between “length” or “distance” and “position” • Representing a position mathematically. University of Maryland

Coordinates and Vectors • Set up a coordinate system • Pick an origin • Pick 3 perpendicular directions • Choose a measurement scale • Each point in space in then specified by three numbers: the x, y, and z coordinates. • The position vector for a particular position is an arrow drawn from the origin to that position. University of Maryland

Motion along a straight line (1-d coordinates) • We specify which direction we are talking about by drawing a little arrow of unit length in the positive direction. • We specify that we are talking about this arrow in symbols by writing • A position a distance x from the origin is written • Note that if x is negative, it means a vector pointing in the direction opposite to University of Maryland

Describing Motion: Time • Time — if we’re to describe something moving we need to tell when it is where it is. • Time is a coordinate just like position • We need an origin (when we choose t = 0) • a direction (usually times later than 0 are +) • a scale (seconds, years, millennia) • Note the difference between • clock reading • a time interval This is like the difference between position and length! University of Maryland

Writing the math • Position at a clock time t:(if we want to emphasizethe direction) • Position at a clock time t:(if we don’t) • Change in position betweentwo times (t1 and t2): • Time interval: University of Maryland

Graphing Position • Describe where something is in terms of its coordinate at a given time. University of Maryland

Displacement • The displacement is the total change in position. • If you make one change and then go back, it could cancel out the first change. University of Maryland

Displacement Isn’t Distance • The displacement of an object is not the same as the distance it travels • Example: Throw a ball straight up and then catch it at the same point you released it • The distance is twice the height • The displacement is zero University of Maryland

C A B x 0 5 10 15 feet Below is shown a straight track along which a toy train can move. If the train moves from point A to point C and then back to point B, what is its resulting displacement (in feet)? • 2 feet • 3 feet • 5 feet • 12 feet • None of the above

Average Velocity • We need to keep track not only of the fact that something has moved but how long it took to get there. • Define the average velocity by University of Maryland

Uniform motion • If an object moves so that it changes its position by the same amount in each unit of time, we say it is in uniform motion. • This means the average velocity will be the same no matter what interval of time we choose. University of Maryland

Instantaneous velocity • Sometimes (often) an object will move so that it is not in uniform motion. Sometimes it moves faster, sometimes slower, sometimes not at all. • We want to be able to describe this change in motion also. • If we consider small enough time intervals, the motion will look uniform — for a little while at least. University of Maryland

Graphing Velocity • An object in uniform motion has constant velocity. • This means the instantaneous velocity does not change with time. Its graph is a horizontal line. • You can see this by putting your mind in “velocity mode” and running a mental movie. University of Maryland

Physics 121: Fundamentals of Physics I