Circular Motion & Universal Gravitation Chapter 7 Circular Motion & Universal Gravitation

Rotation and Revolution Rotation (spin) - spin about an axis located within the body. Ex: ballerina Revolution - object turns about an external axis. Ex: moon around the earth

Uniform Circular Motion Continues in a circle with the same tangential velocity What keeps it going in a circle? Any acceleration?

Uniform Circular Motion Centripetal (center seeking) vs. Centrifugal (towards outside)

Uniform Circular Motion Hammer throw/sling Space station Water glass

Uniform Circular Motion Centripetal acceleration depends on tangential velocity and radius acent = vtangent2/r

Uniform Circular Motion Centripetal Force F = ma, so Fcent = acent*mass Fcent = (mv2)/r Force must come from something else, IT IS A NET FORCE!!!!!! Can be tension (Ball on string), normal (washing machine), friction (ramp)

Uniform Circular Motion Mini-lab Finding the Force in the string

Coriolis Effect Hurricanes Warships Toilets? https://www.youtube.com/watch?annotation_id=annotation_2407455035&feature=iv&src_vid=BiBrV4Q9NYE&v=mXaad0rsV38

Why do things fall? Greeks levity (smoke, helium balloons) vs. gravity (rocks, apples) Gave us the term, but not why

Understanding the Heavens Ancients thought heavens very different from earth Tycho Brahe devoted his life to taking careful measurements and records of the motion of planets, stars, and comets

Understanding the Heavens Johannes Kepler became an assistant of Tycho After Tycho died, Kepler used his extensive data to formulate 3 laws about planetary motion

Kepler’s Laws The paths of the planets are ellipses with the center of the sun at 1 foci A planet sweeps out equal area in equal time intervals

Kepler’s Laws  

Kepler’s Laws Soon after Kepler published his laws Galileo made detailed observations of Jupiter’s 4 largest moons through the first telescope Io – 4.2 unit radius, 1.8 day period Ganymede – 10.7 unit radius, ?? period

Universal Gravitation Newton took Kepler’s ellipse idea and calculated the force on the planet must be proportional to 1/d2 Further reflection, (apple) led him to conclude F also depended on the masses involved

Universal Gravitation F = G*m1*m2/d2 G is universal gravitational constant This is an inverse square law, (butter gun)

Universal Gravitation Newton’s Law of Universal Gravitation confirmed Kepler’s 3rd law Newton didn’t know G and couldn’t find it from the planets since he didn’t know the mass of any of them

Cavendish’s Experiment Weighing the Earth Cavendish found G by using 2 known masses and arranging the experiment carefully so he could measure the (tiny) force With G and the mass of any object on earth he could find the earth’s mass

Weighing the Earth F = G*m1*m2/d2 On the surface of the earth G, Me, and the radius don’t change Only the 2nd mass changes G*Me/r2 = g Ergo: Fg = mg

Orbiting objects Newton’s cannon Objects orbit because gravity supplies a centripetal force G*Mem/r2 = mv2/r Solve for velocity of a satellite Solve for the period of the satellite

Orbiting objects v = √(GMe/r) T = 2π√(r3/(GMe)) These 2 equations will work for any orbiting body, as long as you put in the right mass for Me and r is the distance between the centers of mass

‘Weightlessness’ Are astronauts weightless? Find the acceleration due to gravity when the shuttle is in orbit 200 km above the earth’s surface Weightlessness does not necessarily mean no gravity, freefall creates weightlessness also

Tides Moon caused by gravity differences Remember 2! High tides a day Low tides a day Spring tides a month Neap tides a month https://www.youtube.com/watch?v=u3LtEF9WPt4 seen https://www.youtube.com/watch?v=pwChk4S99i4 explained

The strange force Gravity Gravity, unlike many other forces is not a contact force What supplies the force?-no string Gravitational field Borrows an idea from magnetism and electricity

The strange force Gravity Einstein was not satisfied with field idea Einstein proposed that gravity was simply a result of curved space

The evidence This would require light to be curved by gravity Demonstrated in 1919 by an eclipse experiment