1. Gravity

2. Wait, what does gravity have to do with rotational motion? Let’s look at some well-known physicists and their work to find the answer.

3. Johannes Kepler 1600’s Kepler observed the motions of the planets He came up with three laws to describe their motion, but he didn’t know WHY they moved the way they did

4. Kepler’s Laws Orbits: All planets move in elliptical orbits with the sun at one focus Areas: A line that connects a planet to the sun sweeps out equal areas in equal times Periods: The square of the period of any planet is proportional to the cube of the semimajor axis of its orbit

5. And then he died

6. Isaac Newton 1600’s Newton did not like the lack of explanation behind Kepler’s laws According to the first law, the Earth and moon should travel in a straight line. – So why do they deviate from this path?

7. Here we go again… So, yeah, Newton got bonked on the head by the apple. He realized that what pulled the apple down is also the same force that pulls the moon towards the Earth. To determine the acceleration of the moon, use rotational kinematics

8. Relationships So because F=ma, force is proportional to mass – Because we have two masses, Earth and moon, the force is proportional to both And, based on the calculations we just did, force is inversely proportional to the square of the distance between two objects

9. The finale Put it all together and: F= G((m 1 m 2 )/r 2 ) where G is a proportionality constant

10. G Newton tried to determine what G was, but was unable to do so. And then he died.

11. Henry Cavendish Hundred years later. Cavendish figured out how to measure G The Cavendish Torsion Balance

12. G So the torque exerted on the wire is the force Fg Therefore, G= 6.67 x 10 -11 N m 2 /kg 2

13. And then he died

14. Gravity So, we have a law of gravity for two objects. Often, it is more beneficial to find the acceleration due to gravity between the objects.

15. Orbits Remember, Kepler described orbits in his laws But, what is an orbit, truly?

16. Orbits Suppose we have a ridiculously high mountain on Earth. This mountain has a cannon. The cannon fires a cannonball.

17. Orbits Due to gravity, the cannonball is falling towards Earth, so it lands some distance away from the mountain. But, what if we up the amount of gunpowder?

18. Orbits In theory, you can fire the cannonball with enough force so that it never touches the ground. Now, what if you hitched a ride?

19. Orbits If you rode the cannonball, odds are you’d feel like you’re falling down. That’s what we call free fall. You’d find yourself falling alongside the cannonball.

20. Orbits But again, you’d never hit the Earth. The cannonball hasn’t escaped Earth’s gravitational pull, but it’s balanced out by the speed of the cannonball.

22. Escape! Based on this, there are two ways to escape Earth’s gravity. – Get to a really high altitude. Practically, you want to be less than 100 miles above the Earth; then friction lessens – Go fast. REALLY fast. This is called the escape velocity: