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n 1. An industrial flywheel has a greater rotational inertia when most of its mass is n (a) nearest the axis. n (b) nearest the rim. n (c) uniformly spread out as in a disk.

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n 2. A ring and a disk both of the same mass, initially at rest, roll down a hill together. The one to reach the bottom first n (a) is the disk. n (b) is the ring. n (c) both reach the bottom at the same time.

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n 3. Put a pipe over the end of a wrench when trying to turn a stubborn nut on a bolt, to effectively make the wrench handle twice as long, you'll multiply the torque by n (a) two. n (b) four. n (c) eight.

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Chapter 9 Gravity

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Newton’s law of gravitation n Attractive force between all masses n Proportional to product of the masses n Inversely proportional to separation distance squared n Explains why g=9.8m/s 2 n Provides centripetal force for orbital motion

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Newton’s Law of Universal Gravitation n From Kepler's 3rd Law, Newton deduced inverse square law of attraction. G=6.67 N m 2 /kg 2 G=6.67 N m 2 /kg 2

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Gravity Questions n Did the Moon exert a gravitational force on the Apollo astronauts? n What kind of objects can exert a gravitational force on other objects? n The constant G is a rather small number. What kind of objects can exert strong gravitational forces?

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Gravity Questions n If the distance between two objects in space is doubled, then what happens to the gravitational force between them? n What is the distance is tripled? n …is quadrupled? n What if the mass of one of the object is doubled? n …tripled? n …quadrupled?

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Weight and Weightlessness n Weight »the force due to gravity on an object »Weight = Mass Acceleration of Gravity »W = m g n “Weightlessness” - a conditions wherein gravitational pull appears to be lacking –Examples: »Astronauts »Falling in an Elevator »Skydiving »Underwater

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Ocean Tides n The Moon is primarily responsible for ocean tides on Earth. n The Sun contributes to tides also. n What are spring tides and neap tides?

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Sun Earth New MoonFull Moon Spring Tides

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Sun Earth First Quarter Last Quarter Neap Tides

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BLACK HOLES 4Let’s observe a star that is shrinking but whose mass is remaining the same. 4What happens to the force acting on an indestructible mass at the surface of the star? SFA

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R2R2 F R2R2 F R2R2 F R2R2 F R R R R Remember that the force between the two masses is given by

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4If a massive star shrinks enough so that the escape velocity is equal to or greater than the speed of light, then it has become a black hole. 4Light cannot escape from a black hole. BLACK HOLES

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Einstein’s Theory of Gravitation n Einstein perceived a gravitational field as a geometrical warping of 4-D space and time.

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Near a Black Hole

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n 4. Which is most responsible for the ocean tides? n (a) ships n (b) continental drift n (c) the moon n (d) the sun

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n 5. If the sun were twice as massive n (a) the pull of the earth on the sun would double. n (b) its pull on the earth would double. n (c) both of these. n (d) neither of these

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n 14. The car moving at 50 kilometers/hour skids 10 meters with locked brakes. How far will the car skid with locked brakes if it is traveling at 150 kilometers/hour? n (a) 20 meters n (b) 60 meters n (c) 90 meters n (d) 120 meters n (e) 180 meters

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n 16. When a car is braked to a stop, its kinetic energy is transformed to n (a) stopping energy. n (b) potential energy. n (c) heat energy. n (d) energy of rest.

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End of Chapter 9

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Pythagoras (550 BC) n Claimed that natural phenomena could be described by mathematics

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Aristotle (350 BC) n Asserted that the universe is governed by physical laws

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n The ancient Greeks believed that the earth was at the center of a revolving sphere with stars on it.

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n The Geocentric Model implies Earth-Centered Universe.

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Copernicus(1500's) n Developed a mathematical model for a Sun-centered solar system

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Tycho Brahe (1500's) n Made precise measurements of the positions of the planets

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Kepler(1600's) n Described the shape of planetary orbits as well as their orbital speeds

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Kepler’s First Law n The orbit of a planet about the Sun is an ellipse with the Sun at one focus.

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Kepler’s Second Law n A line joining a planet and the Sun sweeps out equal areas in equal intervals of time.

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Kepler’s Third Law n The square of a planet's orbital period is proportional to the cube of the length of its orbit's semimajor axis. n Or simply… T 2 = R 3 if T is measured in years and R is measured in astronomical units.

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An Astronomical Unit... n …is the average distance of the Earth from the Sun. n 1 AU = 93,000,000 miles = 8.3 lightminutes

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Kepler’s Laws n These are three laws of physics that relate to planetary orbits. n These were empirical laws. n Kepler could not explain them.

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Kepler’s Laws...Simply (See page 192.) n Law 1: Elliptical orbits… n Law 2: Equal areas in equal times… n Law 3: T 2 = R 3

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