2Uniform Circular Motion Motion of an object travelling at constant speed in a circleLet’s explore the kinematics of circular motion.Why is it accelerating, if the speed is constant?What would cause an object to move in a circle?
3What is Centripetal Force? Objects move in a straight line at a constant speed unless a force acts on them. This is Newton's First Law.However, many things move in curved paths, especially circles, and so there must be a force actingon them to pull them outof their straight line pathsand make them turncorners.
4What Does Centripetal Force Depend On? We call the force that makes objects move in a circle the CENTRIPETAL FORCE(the name comes from Latin and means centre-seeking)How is Centripetal Force related to:Mass of object?Velocity of object?Radius size of circle?Let’s Explore!
5Uniform circular motion The speed stays constant, but the direction changesvRThe acceleration in this case is calledcentripetal acceleration
6Wide turns and tight turns little Rbig Rfor the same speed, the tighter turn requires moreacceleration
7Let’s Determine the Velocity of an Object Travelling in a Circle… Remember: Speed = Distance/TimeLet’s define Period (T) as the time it takes the object to travel once around the circle.How far does it travel in one rotation?Therefore:
8path of ball if the string Ball on a stringThe tension in the stringprovides the necessarycentripetal force to keepthe ball going in a circle.path of ball if the stringbreaks
9ExampleWhat is the tension in a string used to twirl a 0.3 kg ball at a speed of 2 m/s in a circle of 1 meter radius?Force = mass x acceleration [ m aC ]acceleration aC = v2 / R = (2 m/s)2/ 1 m= 4 m/s2force = m aC = 0.3 4 = 1.2 NIf the string is not strong enough to handle this tension it will break and the ball goes off in a straight line.
10Motion On A Flat CurveOn a flat, level curve, the friction between the tires and the road supplies the centripetal force.If the tires are worn smooth or the road is icy or oily, this friction force will not be available.The car will not be able to move in a circle, it will keep going in a straight line and therefore go off the road.
11What’s this Centrifugal force ? ? The red object will make the turn only if there is enough friction on itOtherwise it goes straightThe apparent outward force is called the centrifugal forceIt is NOT A REAL force!An object will not move in a circle until something makes it, in this case the car door!object onthe dashboardstraight lineobject naturallyfollows
12What is Gravitational Force? Sir Isaac Newton discovered that every particle attracts every other particle in the universe with a force when he saw an apple fall from a tree towards the earth.The force of attraction between any two particles in the universe is called Gravitation or gravitational force
13Newton’s Law of Universal Gravitation G is the universal gravitational constant and equals x Nm2 / kg2
14G vs. g Always distinguish between G and g G is the universal gravitational constantIt is the same everywhereg is the acceleration due to gravityg = 9.80 m/s2 at the surface of the Earthg will vary by location
15Why doesn’t the moon fall into the earth? The moon is actually falling toward Earth but has great enough tangential velocity to avoid hitting Earth.If the moon did not fall, it would follow a straight-line path.
17Johannes Kepler 1571 – 1630 German astronomer Best known for developing laws of planetary motionBased on the observations of Tycho Brahe
18Kepler’s Laws Kepler’s First Law Kepler’s Second Law All planets move in elliptical orbits with the Sun at one focusKepler’s Second LawThe radius vector drawn from the Sun to a planet sweeps out equal areas in equal time intervalsKepler’s Third LawThe square of the orbital period of any planet is proportional to the cube of the semimajor axis of the elliptical orbit
19Kepler’s Third Law Can be predicted from the inverse square law Start by assuming a circular orbitThe gravitational force supplies a centripetal forceKs is a constant
20Mass of the SunUsing the distance between the Earth and the Sun, and the period of the Earth’s orbit, Kepler’s Third Law can be used to find the mass of the SunSimilarly, the mass of any object being orbited can be found if you know information about objects orbiting it