Comments about HW #1•Sunset observations:•Pick a convenient spot (your dorm?)•Try to get 1 data point per week•Keep a “lab notebook” with date,time, weather, comments•Mark down bad weather attemptsToday: Some PhysicsbackgroundJust what you need to knowIsaac Newton (1642-1727)• Isaac Newton described thefundamental laws covering themotion of bodies• Had to invent his own mathematics(Calculus) to do it!• His work is used even today incalculating everything from how fasta car stops when you apply thebrakes, to how much rocket fuel touse to get to Saturn!• And he did most of it before his 24thbirthday…Newton’s First Law• An object in uniform motion willstay in motion, an object at restwill stay at rest.• If an object’s velocity is notchanging, either there are noforces acting on it, or the forcesare balanced and cancel eachother out– Hold a ball out in your hand, and notethat it is not moving– Force of gravity (downward) isbalanced by the force your handapplies (upward)!• Note: Velocity has a speed (I.e. 60mph) and a direction (I.e.NW).• If an object’s velocity is changing,there must be forces present!– Dropping a ball– Applying the brakes in a car• This change can be either speed ordirection or BOTH!Mass and Inertia• Mass is described by the amountof matter an object contains.• This is different from weight –weight requires gravity or someother force to exist!• Ex: while swimming, your weightmay feel less because the bodyfloats a little. Your mass,however, stays the same!• Inertia is simply the tendency ofmass to stay in motion• Newton’s First Law is sometimescalled the Law of Inertia:Acceleration• The term acceleration isused to describe the changein a body’s velocity over time– Stepping on the gas pedalof a car accelerates the car– it increases the speed– Stepping on the brakesdecelerates a car – itdecreases the speed• A change in an object’sdirection of motion is alsoacceleration– Turning the steering wheelof a car makes the car goleft or right – this is anacceleration!– Forces must be present ifacceleration is occurringNewton’s Second Law• The force (F) acting on an objectequals the product of its acceleration(a) and its mass (m)• F = m × a• We can rearrange this to be:• a = F/m• For an object with a large mass, theacceleration will be small for a givenforce• If the mass is small, the same forcewill result in a larger acceleration!• Though simple, thisexpression can be used tocalculate everything fromhow hard to hit the brakes tohow much fuel is needed togo to the Moon!Mass vs Force• Mass is measured in Kg in the Metric system (mks) andslugs in the English system.• I slug = 32.2 lbs (on Earth)• Force is measured in Newtons in mks and pounds in theEnglish system.• Why do I know my weight in Kg and in pounds?Newton’s Third Law• When two bodies interact, theycreate equal and opposite forceson each other• If two skateboarders have thesame mass, and one pushes onthe other, they both move awayfrom the center at the samespeed• If one skateboarder has moremass than the other, the samepush will send the smallerperson off at a higher speed,and the larger one off in theopposite direction at a smallerspeed– Why?This works for planets, too!Circular Motion• Tie a string to a ball andswing it around your head– Law of inertia says that theball should go in a straightline– Ball goes in a circle – theremust be forces!• Where’s the force?– It’s the tension in the stringthat is changing the ball’svelocity– If the string breaks, the ballwill move off in a straightline (while falling to theground)Centripetal Force• If we tie a mass to a string andswing the mass around in acircle, some force is required tokeep the mass from flying off ina straight line• This is a centripetal force, aforce directed towards thecenter of the system• The tension in the stringprovides this force.• Newton determined that thisforce can be described by thefollowing equation:dVmFC2!=dVmFC2!=Conservation of Angular momentumChange in Angular momentum =0For a closed system! p = mvConservation of momentumChange in momentum =0For a closed system! L = mvrDefinition of Angular Momentum• Angular momentum is the rotational equivalent of inertia• Can be expressed mathematically as the product of the objectsmass, rotational velocity, and radius• If no external forces are acting on an object, then its angularmomentum is conserved, or a constant:constant=!!= rVmLConservation of AngularMomentum• Since angular momentum isconserved, if either the mass, sizeor speed of a spinning objectchanges, the other values mustchange to maintain the samevalue of momentum– As a spinning figure skater pulls herarms inward, she changes her valueof r in angular momentum.– Mass cannot increase, so herrotational speed must increase tomaintain a constant angularmomentum• Works for stars, planets orbitingthe Sun, and satellites orbiting theEarth, too!Orbital Motion and Gravity• Astronauts in orbit around the Earthare said to be in free fall, aweightless state.– Are they falling? Yes!• Imagine a cannon on top of amountain that fires a cannonballparallel to the ground• The cannonball leaves the cannonand is pulled toward the ground bygravity• If the ball leaves the cannon with a slowvelocity, it falls to the ground near themountain• If the cannonball has a higher velocity, iffalls farther from the mountain.• What if we gave the cannonball a verylarge velocity, so large that it “misses” theEarth?• The cannonball would be in orbit aroundthe Earth, and it would be falling!Newton’s Universal Law ofGravitation• Every mass exerts a force ofattraction on every other mass.The strength of the force isproportional to the product of themasses divided by the square ofthe distance between them– Simply put, everything pulls oneverything else– Larger masses have a greater pull– Objects close together pull moreon each other than objects fartherapart• This is true everywhere, and forall objects– The Sun and the planets exert agravitational force on eachother– You exert a gravitational forceon other people in the