EVERYTHING MOVES!!!!! THERE IS NO APSOLUTE REST!!!! together with the whole galaxy moving away from the center of the Universe at huge speed. Measurements, confirmed by the Cosmic Background Explorer satellite in 1989 and 1990, suggest that our galaxy and its neighbors, are moving at 600 km/s (1.34 million mi/h) in the direction of the constellation Hydra.). together with the whole galaxy moving away from the center of the Universe at huge speed. Measurements, confirmed by the Cosmic Background Explorer satellite in 1989 and 1990, suggest that our galaxy and its neighbors, are moving at 600 km/s (1.34 million mi/h) in the direction of the constellation Hydra.). Even while sitting in the classroom appearing motionless, you are moving very fast. 0.4 km/s (0.25 mi/s) rotating around the center of the Earth 0.4 km/s (0.25 mi/s) rotating around the center of the Earth 30 km/s relative to the Sun 30 km/s relative to the Sun even faster relative to the center of our galaxy (The Sun orbits the center of the Milky Way at about 250 km/s and it takes about 220 million years to complete an orbit. ) even faster relative to the center of our galaxy (The Sun orbits the center of the Milky Way at about 250 km/s and it takes about 220 million years to complete an orbit. ) The Sea Serpent

When you say that you drove your car at speed of 50 mi/h, of course you mean relative to the road or with respect to the surface of the Earth. You are actually using coordinate system without knowing it. When we discuss the motion of something, we describe its motion relative to something else. A frame of reference is a perspective from which a system is observed together with a coordinate system used to describe motion of that system.

One of the important problem problems in Physics is this: if a any given instant in time we know the positions and velocities of all the particles that make up a particular system can we predict the future position and velocities of all the particles? If we can do it then we can: predict solar eclipses, put satellites into orbit, find out how the position of a swing varies with time and find out where a soccer ball ends up when struck by a foot. Classical Mechanics: - Study of the motion of macroscopic objects and related concepts of force and energy Kinematics – is concerned with the description of how objects Kinematics – is concerned with the description of how objects move; their motion is described in terms of displacement, move; their motion is described in terms of displacement, velocity, and acceleration velocity, and acceleration Dynamics – explains why objects change the state of the motion Dynamics – explains why objects change the state of the motion (velocity) as they do; explains motion and causes of changes using (velocity) as they do; explains motion and causes of changes using concepts of force and energy. concepts of force and energy.

The movement of an object through space can be quite complex. There can be internal motions, rotations, vibrations, etc… This is the combination of rotation (around its center of mass) and the motion along a line - parabola. If we treat the hammer as a particle the only motion is translational motion (along a line) through space.

Kinematics in One Dimension Our objects will be represented as point objects (particles) so they move through space without rotation. We’ll be neglecting all factors such as the shape, size, etc. that make the problem too difficult for now. Simplest motion: motion of a particle along a line – called: translational motion or one-dimensional (1-D) motion.

“+” direction Distance between final and initial point Displacement Example: 1) x 1 = 7 m, x 2 = 16 m x 3 = 12 m ∆x = 5 m of an object is the shortest distance from its the initial to the final position of an object is the shortest distance from its the initial to the final position.  The displacement tells us how far an object is from its starting position and in what direction its starting position and in what direction 2) x 1 = 7 m, x 2 = 2 m ∆ x = - 5 m “ – ” direction Representation of displacement in a coordinate system path; length is distance traveled Pdisplacement Q

A racing car travels round a circular track of radius 100 m. Example: The car starts at O. When it has travelled to P its displacement as measured from O is A 100 m due East B 100 m due West C 100 √2 m South East D 100 √2 m South West

Scalar is a quantity that is completely specified by a positive or negative number with appropriate units. Temperature, length, mass, time, speed, … Temperature, length, mass, time, speed, … Vector must be specified by both magnitude (number and unit) and direction. Displacement, velocity, force,… Displacement, velocity, force,… Vectors and Scalars Each physical quantity will be either a scalar or a vector. Scalar Vector distance - 50 km displacement: 50 km, E speed - 70 km s -1 velocity: 70 km s -1, S-W Scalars obey the rules of ordinary algebra: 2 kg of potato + 2 kg of potato = 4 kg of potato Vectors obey the rules of vectors’ algebra: The sum of two vectors depends on their directions.

DEF: Average velocity is the displacement covered per unit time. Average and Instantaneous Velocity (it obviously has direction, the same as displacement) Instantaneous velocity is the velocity at one instant. The speedometer of a car reveals information about the instantaneous speed of your car. It shows your speed at a particular instant in time. If direction is included you have instantaneous velocity. SI unit : m/s

Average and Instantaneous Speed How fast do your eyelids move when you blink? Displacement is zero, so v avg = 0. How fast do you drive in one hour if you drive zigzag and the magnitude of the displacement is different from distance? To get the answers to these questions we introduce speed: it tells us how fast the object is moving Speed is the distance object covers per unit time.

KCR train has travelled a distance of about 6.7 km from University Station to Tai Po Market Station. But if we measure their separation by drawing a straight line on the map, we will find that Tai Po Market Station is only 5.4 km from University Station, roughly in the North- West direction. This is the displacement of the train. We take the KCR trip from University Station to Tai Po Market Station. It takes about 6 minutes to travel a distance of 6.7 km. Thus, The displacement of Tai Po Market Station from University Station is 5.4 km, so in the North-West direction. This is smaller than the average speed of the train. So why do we care of velocity at all? OK, it gives us direction what is very important (just imagine airplane controller with information only on speed of airplanes not on directions). But we saw that average speed is greater in general than magnitude of average velocity. So why is concept of velocity so important?

if motion is 1-D without changing direction; speed = magnitude of velocity because speed = magnitude of velocity because distance traveled = magnitude of displacement instantaneous speed = magnitude of instantaneous velocity Because acceleration is a vector, all of equations are vector equations Because acceleration is a vector, all of equations are vector equations. Acceleration can be in any direction to the velocity and the motion will depend on that. ONLY:

A racing car travels round a circular track of radius 100 m. Example: The car starts at O. It travels from O to P in 20 s. Its velocity was Its speed was 10 m/s. πr/t = 16 m/s. The car starts at O. It travels from O back to O in 40 s. Its velocity was Its speed was 0 m/s. 2πr/t = 16 m/s.

Let’s look at the motion with constant velocity so called uniform motion in that case, velocity is the same at all times so v = v avg at all times, therefore: or x = vt This is the only equation that we can use for the motion with constant velocity. Object moving at constant velocity covers the same displacement in the same interval of time. click

In the SI system the unit is meters per second per second. Acceleration Acceleration is the change in velocity per unit time. a = 3 m/s 2 means that velocity changes 3 m/s every second!!!!!! If an object’s initial velocity is 4 m/s then after one second it will be 7 m/s, after two seconds 10 m/s, …. (Change in velocity ÷ time taken) vector quantity – direction of the change in velocity

Let’s look at the motion with constant acceleration so called uniformlly accelerated motion t = the time for which the body accelerates t = the time for which the body accelerates a = acceleration u = the velocity at time t = 0, the initial velocity v = the velocity after time t, the final velocity x = the displacement covered in time t let:

from definition of a: velocity v at any time t = initial velocity u increased by a, every second  t(s) v (m/s) example: u = 2 m/s a = 3 m/s 2 speed increases 3 m/s EVERY second. In general: for the motion with constant acceleration: for the motion with constant acceleration: → v = u + at arithmetic sequence, so

Till now we had three formulas From definition of average velocity we can find displacement in any case: v = u + at x = v avg t For motion with constant acceleration, velocity changes according: and average velocity is: These three equations are enough to solve any problem in motion with constant acceleration. But we are lazy and we want to have more equations that are nothing new, but only manipulations of this three.

v = u + at v 2 = u 2 + 2ax v so we got them !!!! →

Uniform Accelerated Motion – all together 1 – D Motion with Constant Acceleration v = u + at v 2 = u 2 + 2ax x = v avg t for any motion In addition to these equations to solve a problem with constant acceleration you’ll need to introduce your own coordinate system, because displacement, velocity and acceleration are vectors (they have directions).

So beware: both velocity and acceleration are vectors. Therefore 1. if velocity and acceleration (change in velocity) are in the same direction, speed of the body is increasing. 2. if velocity and acceleration (change in velocity) are in the opposite directions, speed of the body is decreasing. 3. If a car changes direction even at constant speed it is accelerating. Why? Because the direction of the car is changing and therefore its velocity is changing. If its velocity is changing then it must have acceleration. This is sometimes difficult for people to grasp when they first meet the physics definition of acceleration because in everyday usage acceleration refers to something getting faster. Acceleration can cause: 1. speeding up 2. slowing down 3. and/or changing direction 3. and/or changing direction

A stone is rotating around the center of a circle. The speed is constant, but velocity is not – direction is changing as the stone travels around, therefore it must have acceleration. Velocity is tangential to the circular path at any time. ACCELERATION IS ASSOCIATED WITH A FORCE!!! The force (provided by the string) is forcing the stone to move in a circle giving it acceleration perpendicular to the motion – toward the CENTER OF THE CIRCLE - along the force. This is the acceleration that changes velocity by changing it direction only. When the rope breaks, the stone goes off in the tangential straight- line path because no force acts on it.

blue arrow – velocity red arrow – acceleration In the case of moon acceleration is caused by gravitational force between the earth and the moon. So, acceleration is always toward the earth. That acceleration is changing velocity (direction only). 1. weakening gravitational force would result in the moon getting further and further away still circling around earth. 3. The moon has no speed – it moves toward the earth – accelerated motion in the straight line - crash 4. High speed – result the same as in the case of weakening gravitational force 2. no gravitational force all of a sudden: there wouldn’t be acceleration – therefore no changing the velocity (direction) of the moon, so moon flies away in the direction of the velocity at that position ( tangentially to the circle). Only the right speed and acceleration (gravitational force) would result in circular motion!!!!!!!

THE PHYSICS CLASSROOM