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Gravity

Gravity. Gravity. 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. Johannes Kepler. 1600’s Kepler observed the motions of the planets

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Gravity

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  1. Gravity

  2. Gravity • 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((m1m2)/r2) 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 10-11N m2/kg2

  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.

  21. 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:

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