Reative Veocity Two observers moving reative to each other generay do not agree on the outcome of an experiment However, the observations seen by each are reated to one another A frame of reference can described by a Cartesian coordinate system for which an observer is at rest with respect to the origin
Different Measurements, exampe Observer A measures point P at +5 m from the origin Observer B measures point P at +10 m from the origin The difference is due to the different frames of reference being used
Different Measurements, another exampe The man is waking on the moving betway The woman on the betway sees the man waking at his norma waking speed The stationary woman sees the man waking at a much higher speed The combination of the speed of the betway and the waking The difference is due to the reative veocity of their frames of reference
Reative Veocity, generaized Reference frame S A is stationary Reference frame S B is moving to the right! reative to S A at This aso means! that S A moves at reative to S B v BA v AB Define time t = 0 as that time when the origins coincide
Notation The first subscript represents what is being observed The second subscript represents who is doing the observing Exampe! v AB The veocity of A as measured by observer B
Reative Veocity, equations The positions as seen from the two reference frames are reated through the veocity! r PA = r! PB + v! BA t The derivative of the position equation wi give the veocity equation! u PA = u! PB + v! BA!! u PA u PB is the veocity of the partice P measured by observer A is the veocity of the partice P measured by observer B These are caed the Gaiean transformation equations Specia Reativity veocity addition ( ):
Acceeration in Different Frames of Reference The derivative of the veocity equation wi give the acceeration equation The acceeration of the partice measured by an observer in one frame of reference is the same as that measured by any other observer moving at a constant veocity reative to the first frame.
The Laws of Motion
Sir Isaac Newton 25 Dec 1642 31 Mar 1727* (84 years od) Formuated basic aws of mechanics Discovered Law of Universa Gravitation Invented cacuus Many observations deaing with ight and optics * Add 11 days for modern caendar
Engraving made from 1726 painting by John Vanderbank Newton aged 46. Eariest portrait, painted in 1689 by Godfrey Kneer Death mask 1727 Aged 84
Woosthorpe Manor and appe tree 1820 1666 notes by John Conduit, first mention of appe and gravity! (when Newton was 24) He first thought of his system of gravitation which he hit upon by observing an appe fa from a tree Woosthorpe Manor and appe tree 1998
Newton performing his prism experiment. Painting by Sascha Grusche (2015) Newton s bedroom at Woosthorpe Mannor today
Physics Word po 1999 - Who is the greatest physicist ever?
Some of Isaac Newton s sins, he isted himsef in 1662, aged 19 Negecting to pray Faing out with the servants Punching my sister Making a mousetrap on a Sunday morning Eating an appe in church Robbing my mother s box of pums and sugar Peevishness with my mother (peevish = being angry) Swimming in a kimne on Thy day (kimne=a vesse for water, e.g. a trough) Caing Dorothy Rose a jade (disreputabe or bad-tempered) Denying a crossbow to my mother and grandmother athough I knew of it Peevishness over a piece of bread and butter at Mr Cark s Steaing cherry cobs from Edward Storer (cob=piece of wood? Buiding materia? For some experiment he was doing?) Beating Arthur Storer Putting a pin in John Keys hat to prick him Threatening my father and mother to burne them and the house over them Having uncean thoughts
Force Forces are what cause any change in the veocity of an object Newton s definition A force is that which causes an acceeration
Casses of Forces Contact forces invove physica contact between two objects Exampes a, b, c Fied forces act through empty space No physica contact is required Exampes d, e, f
Fundamenta Forces Gravitationa force Between objects Eectromagnetic forces * Between eectric charges Nucear force Between subatomic partices Weak forces Arise in certain radioactive decay processes Note: These are a fied forces * Barrow & Webb: http://www.scientificamerican.com/artice.cfm?id=inconstant-constants&ref=sciam
More About Forces A spring can be used to caibrate the magnitude of a force Doubing the force causes doube the reading on the spring When both forces are appied, the reading is three times the initia reading
Vector Nature of Forces The forces are appied perpendicuary to each other The resutant (or net) force is the hypotenuse Forces are vectors, so you must use the rues for vector addition to find the net force acting on an object
Newton s First Law If an object does not interact with other objects, it is possibe to identify a reference frame in which the object has zero acceeration This is aso caed the aw of inertia It defines a specia set of reference frames caed inertia frames We ca this an inertia frame of reference
Inertia Frames Any reference frame that moves with constant veocity reative to an inertia frame is itsef an inertia frame A reference frame that moves with constant veocity reative to the distant stars is the best approximation of an inertia frame We can consider the Earth to be such an inertia frame, athough it has a sma centripeta acceeration associated with its motion
Newton s First Law Aternative Statement In the absence of externa forces, when viewed from an inertia reference frame*, an object at rest remains at rest and an object in motion continues in motion with a constant veocity Newton s First Law describes what happens in the absence of a force Does not describe zero net force Aso tes us that when no force acts on an object, the acceeration of the object is zero * A non-acceerating reference frame
Inertia and Mass The tendency of an object to resist any attempt to change its veocity is caed inertia Mass is that property of an object that quantifies how much resistance an object exhibits to changes in its veocity Masses can be reated to the acceerations produced by a given force acting on them: m 1 = a 2 m 2 a 1 The magnitude of the acceeration acting on an object is inversey proportiona to its mass
More About Mass Mass is an inherent property of an object Mass is independent of the object s surroundings Mass is independent of the method used to measure it Mass is a scaar quantity The SI unit of mass is kg
Mass vs. Weight Mass and weight are two different quantities Weight is equa to the magnitude of the gravitationa force exerted on the object Weight wi vary with ocation Exampe: w earth = 180 b; w moon ~ 30 b m earth = 2 kg; m moon = 2 kg
What is mass? Gravitationa mass, a characteristic constant of the partices experiencing a gravitationa force Gravitationa force F = Gm g1 m g 2 r 2 Inertia force F = ma Inertia mass, a different characteristic constant of the acceerated partice DOES GRAVITATIONAL MASS INTERTIAL MASS =1? Answer: Yes macroscopicay; Maybe not quantum mechanicay! http://www.technoogyreview.com/view/419367/new-quantum-theory-separates-gravitationa-and-inertia-mass/
Newton s Second Law When viewed from an inertia reference frame, the acceeration of an object is directy proportiona to the net force acting on it and inversey proportiona to its mass Force is the cause of change in motion, as measured by the acceeration Agebraicay,! a! F m! F = m! a With a proportionaity constant of 1 and speeds much ower than the speed of ight
More About Newton s Second Law! F is the net force This is the vector sum of a the forces acting on the object Newton s Second Law can be expressed in terms of components: ΣF x = m a x ΣF y = m a y ΣF z = m a z
Units of Force The SI unit of force is the newton (N) 1 N = 1 kg m / s 2
Gravitationa Force The gravitationa force, F g, is the force that the earth exerts on an object This force is directed toward the center of the earth From! Newton s Second Law F g = m g! Its magnitude is caed the weight of the object Weight = F g = mg!
More About Weight Because it is dependent on g, the weight varies with ocation g, and therefore the weight, is ess at higher atitudes This can be extended to other panets, but the vaue of g varies from panet to panet, so the object s weight wi vary from panet to panet Weight is not an inherent property of the object
Gravitationa Mass vs. Inertia Mass In Newton s Laws, the mass is the inertia mass and measures the resistance to a change in the object s motion In the gravitationa force, the mass is determining the gravitationa attraction between the object and the Earth Experiments show that gravitationa mass and inertia mass have the same vaue