Transcript SPIN
SPIN Slides created by Kathy Buckland at the University of British What’s Happening Here? • An example of circular motion What is Circular Motion? • The circular path along which an object travels • The rotation around a fixed axis What is the word used to describe this path? ORBIT Examples • • • • Rollercoaster Swinging an object on a string Planetary objects-moon, satellites, etc. Car going around a round-about Back to the mid 1600’s… Newton’s Second Law: “Mutationem motus proportionalem esse vi motrici impressae, et fieri secundum lineam rectam qua vis illa imprimitur” -Principia Mathematica (1687) Otherwise known as… F ma F=force (N) m=mass (kg) a=acceleration (m/s2) F=ma What is FORCE? • PUSH or a… • PULL Examples of Forces • Gravity • Impact Forces • Tension • Friction Circular Motion and Force How does the object stay in its path? This force is called… CENTRIPETAL FORCE centrum "center" and petere “go to” or “seek” To get where you want “to go”, you must…. PEDAL…. Not a new force !! Examples of forces: • Gravity • Impact Forces • Tension • Friction Examples of these “acting” as the CENTRIPETAL FORCE • Ball on a string • Rollercoaster • Planetary Motion • Car going in circles F ma What next? MASS • The amount of MATTER an object contains • Not weight -weight changes depending on gravitation field F ma and finally… ACCELERATION How the velocity changes in a certain amount of time In physics lingo v a t a=acceleration (m/s2) Δ= “change in” v=velocity (m/s) t=time (s) 2007 Lamborghini Murcielago LP640 acceleration: 0-62 mph time of 3.4 seconds (0-100km/h in 3.4 seconds!) F ma ACCELERATION How the velocity changes in a certain amount of time In physics lingo • • • • a=acceleration (m/s2) Δ= “change in” v=velocity (m/s) t=time (s) v a t • Velocity has a DIRECTION and a MAGNITUDE • The speed is the MAGNITUDE How do we represent direction and magnitude? VECTORS Vector Recall The length of the vector represents the MAGNITUDE or SPEED The direction it points is the DIRECTION Adding: a a+b b Subtracting: a a-b b Back to Circular Motion… F ma How can we find the force it takes to hold on object in orbit? Remember: v a t Δv is a change in direction not magnitude DEMO # 1 Finding centripetal acceleration What will it be? How do we get centripetal acceleration ? A little geometry and algebra… Find similar triangles t2 Three more steps.. 1. Make a tiny triangle so.. • • t1 S=v(t2-t1)=vΔt have a right triangle use sinθ = opposite hypotenuse • sin θ = θ 2. Use similar triangles 3. Use some algebra Centripetal acceleration is… 2 v acent r Finally put it all together… v F ma m t For circular motion… Fcent macent 2 v m r Now What’s Happening Here? • Our starting example of circular motion What to remember • What circular motion is- be able to recognize it • Newton’s Second Law- you will see it again! F ma • That velocity has direction and speed • Centripetal acceleration deals with the change in direction • Things that effect centripetal force are mass, velocity, and the distance from the center 2 Fcent v m r