1. UNIT 6 Circular Motion and Gravitation 1

2. ConcepTest 9.1bBonnie and Klyde II Bonnie Klyde 1) Klyde 2) Bonnie 3) both the same 4) linear velocity is zero for both of them Bonnie sits on the outer rim of a merry- go-round, and Klyde sits midway between the center and the rim. The merry-go-round makes one revolution every two seconds. Who has the larger linear (tangential) velocity?

3. linear speeds v v = R  Bonnie is located further out Their linear speeds v will be different since v = R  and Bonnie is located further out (larger radius R) than Klyde. Bonnie Klyde 1) Klyde 2) Bonnie 3) both the same 4) linear velocity is zero for both of them Bonnie sits on the outer rim of a merry- go-round, and Klyde sits midway between the center and the rim. The merry-go-round makes one revolution every two seconds. Who has the larger linear (tangential) velocity? ConcepTest 9.1bBonnie and Klyde II Follow-up: Who has the larger centripetal acceleration?

4. Units of Chapter 7 Kinematics of Uniform Circular Motion Dynamics of Uniform Circular Motion Newton’s Law of Universal Gravitation Kepler’s Laws and Newton’s Synthesis Torque and Newton’s Laws of Motion 4

5. Newton’s Law of Universal Gravitation If the force of gravity is being exerted on objects on Earth, what is the origin of that force? Newton’s realization was that the force must come from the Earth. He further realized that this force must be what keeps the Moon in its orbit.

6. The gravitational force on you is one-half of a Third Law pair: the Earth exerts a downward force on you, and you exert an upward force on the Earth. When there is such a disparity in masses, the reaction force is undetectable, but for bodies more equal in mass it can be significant. Newton’s Law of Universal Gravitation

7. Therefore, the gravitational force must be proportional to both masses. By observing planetary orbits, Newton also concluded that the gravitational force must decrease as the inverse of the square of the distance between the center of masses. In its final form, the Law of Universal Gravitation reads: where (7-4) Newton’s Law of Universal Gravitation

9. The magnitude of the gravitational constant G can be measured in the laboratory. Newton’s Law of Universal Gravitation The British physicist Henry Cavendish performed an experiment in 1798 that is referred to as “weighing the Earth.” He in fact measured the value of the universal gravitation constant, G.

10. Newton’s Law of Universal Gravitation In the Cavendish experiment, two known masses are suspended from a thin thread. Near each suspended mass is a large stationary mass, M. Each suspended mass is attracted by the force of gravity toward the large mass near it; hence the rod holding the suspended masses tends to rotate and twist the tread. The twist angle can be measured by bouncing a beam of light from a mirror attached to the thread. A measurement of the twist angle gives the magnitude of the force of gravity. Knowing the masses, the force, and the distances from their centers, Cavendish calculated the constant G.

11. Gravity Near the Earth’s Surface; Geophysical Applications Now we can relate the gravitational constant to the local acceleration of gravity. We know that, on the surface of the Earth: Solving for g gives: Now, knowing g and the radius of the Earth, the mass of the Earth can be calculated: (7-5)

12. The acceleration due to gravity varies over the Earth’s surface due to altitude, local geology, and the shape of the Earth, which is not quite spherical. Gravity Near the Earth’s Surface; Geophysical Applications

13. Satellites and “Weightlessness” Satellites are routinely put into orbit around the Earth. The tangential speed must be high enough so that the satellite does not return to Earth, but not so high that it escapes Earth’s gravity altogether.

14. The satellite is kept in orbit by its speed – it is continually falling, but the Earth curves from underneath it. Satellites and “Weightlessness”

15. Objects in orbit are said to experience weightlessness. A gravitational force is acting on them! The satellite and all its contents are in free fall, so there is no normal force. This is what leads to the experience of weightlessness. Satellites and “Weightlessness” At resta up ; 3/2 mga down ; 0 mg

16. More properly, this effect is called apparent weightlessness, because the gravitational force still exists. It can be experienced on Earth as well, but only briefly: Satellites and “Weightlessness”

17. 17 Gravitation Problem Find the distance between a 0.300-kg billiard ball and a 0.400-kg billiard ball, if the magnitude of the gravitational force between them is 8.92 x 10 -11 N.

18. END 18