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• He came up with three laws to describe their

motion, but he didn’t know WHY they moved the way they did

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

And then he died

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?

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

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

The finale

• Put it all together and:F= G((m1m2)/r2)

where G is a proportionality constant

G

• Newton tried to determine what G was, but was unable to do so.

• And then he died.

Henry Cavendish

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

G

• So the torque exerted on the wire is the force Fg

• Therefore, G= 6.67 x 10-11 N m2/kg2

And then he died

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.

Orbits

• Remember, Kepler described orbits in his laws• But, what is an orbit, truly?

Orbits

• Suppose we have a ridiculously high mountain on Earth.

• This mountain has a cannon.• The cannon fires a cannonball.

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?

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?

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.

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.

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: