Motion

Mechanics – branch of physics dealing with the action of forces on objects and with the resulting motion.

Branches of Mechanics Statics: deals with the forces acting stationary objects. Dynamics: studies the motion of objects and the relationship of this motion to forces and mass. Kinematics: Part of dynamics that describes motion without regard to what causes it.

Types of Motion One Dimensional Motion – Motion in a straight line. Constant Velocity – Constant speed in a straight line. Uniform Acceleration – Velocity changes at a constant rate.

History of Mechanics Greeks (Aristotle and Ptolemy) – Geocentric Model Copernicus – Heliocentric Model Galileo – Discoveries with his telescope Kepler – 3 Laws of Planetary Motion Newton – 3 Laws of Motion

Frames of Reference Frame of Reference (Reference Point) - are the objects one uses to determine if motion has occurred and any changes in that motion.

Coordinate Systems 1 Coordinate – on a line 2 Coordinates – in a plane 3 Coordinates – in space

Coordinate Systems Include Fixed reference point or origin. Set of specific axes or directions (scaled and labeled). Ways to label a point in space relative to origin.

Coordinate Systems Cartesian Coordinate System (x,y) Polar Coordinate System (r, ))

Vectors vs. Scalar Quantities Scalar Quantity – Physical Quantity that has magnitude only. (Ex. mass, time, distance, speed). Vector Quantity – Physical Quantity that has both Magnitude and Direction (Ex. displacement, velocity, acceleration).

Ways to Represent Vectors 1.With Arrows 2.With Sign Conventions (+ or -) 3.With Angles (  ) and Definite Directions (N, S, E, or W) Note: Vectors can be represented with a negative sign to show direction.

Time Intervals “  ” (delta) means “change in”  t = Final time – Initial time  t = t f – t i (Most of the time t i = 0)

Distance vs. Displacement Distance – measures the total length of the path traveled (Scalar). Displacement – measures the straight line distance from where you start to where you finish (Vector). S.I. unit for both distance and displacement is meter (m).

Speed Average Speed – the total distance traveled divided by the total time for the trip (Scalar). S.I. Unit is “meter per second” (m/s). speed =  dist/  t Instantaneous Speed – the speed at any particular point of the trip.

Velocity Average Velocity – the total displacement divided by the total time of the trip (Vector). S.I. Unit is “meter per second” (m/s). v =  d/  t Instantaneous Velocity – the slope of the tangent line on a displacement vs. time graph. (Velocity at a specific point)

Acceleration Average Acceleration – is the time rate of change of velocity (Vector). S.I. Unit is “meter/second squared” (m/s 2 ) or “meter per second per second”. a =  v/  t Instantaneous Acceleration – the slope of the tangent line on a velocity vs. time graph. (Acceleration at a specific point)

Ways to Accelerate Note: Acceleration is defined as a change in velocity (vector quantity)! Change in Speed (Magnitude) –Speed up –Slow down Change in Direction

Equations speed =  dist/  tv =  d/  t a =  v/  ta = v f – v i t v f = v i + at

Motion Diagrams Purpose: To break down the problem into smaller component parts that can be isolated and manipulated.

Motion Diagrams 1.Pick a reference point. 2.Identify and represent all variables and directions on your diagram (d, v, a, t). 3.Identify which variables in the problem remain constant or change over time. 4.Remember time keeps going even when the other variables stop!

Question #1 Does an object with negative acceleration have to be slowing down? No!! How about Gravity?

Question #2 Is it possible for an object to have a uniform acceleration (not equal to zero) and have an instantaneous velocity equal to zero? YES!! An object thrown up in the air at its highest point!