AP Physics - Uniform Circular Motion
Rotation
Spinning based on internal axis
Circular Motion
Spinning based on external point
Center seeking
Not centrifugal
Inertia of the object
ΣFc
Can be any type of force
Moving in a circle
384 B.C.E. - 322 B.C.E. Aristotle and Plato
Geocentric
Earth Centered
Believed the heavens were small remote objects in motion around the earth that moved with constant angular rate
310 B.C.E - 230 B.C.E (Aristarches)
Believed that the sun was the center of the universe
Heliocentric
Sun centered
Believed there were spheres for the stars, planets, and Earth
celestial sphere was motionless
earth rotates once on an axis of its own
planets moved in circular paths around the sun
150 C.E. Claudius Ptolemy
Believed both systems could be used in describing motion
Preferred geocentric theory because it fit the causes of motion of the planets, stars, and sun
Believed the earth was the center of the universe but not the center of all the heavenly circles
Ptolemy Model
Developed a very clever and rather accurate procedure for predicting the positions of each planet on a geocentric model
Constructed a model out of circles and three other geometrical devices that would each provide for variations in the rate of angular motion as seen from Earth
Eccentric
Epicycle
Equant
Successes:
Found a combination of motions that gave more accurate predictions on positions of planets to withing 2° over a long period of time
Limitation:
Not possible to calculate the period or the size of each planet’s orbit
1473 - 1543 (Nicolaus Copernicus)
Adopted the heliocentric system with the following assumptions
No precise geometrical circles
Center of the earth was not the center of the universe, but the cause of gravitation for the moon
The distance from the earth to the sun is very small in comparison to the distance to the stars
The earth has more than one motion
It rotates on an axis
It revolves around the sun
Successes (Copernicus was able to calculate):
The period of motion of each planet
The size of each planet’s orbit in comparison to the earth’s orbit
Limitations:
Founded on inaccurate data
1546 - 1601 (Tycho Brahe)
Believed in the geocentric system
Recorded positions of the planets in trying to prove the geocentric theory
Collected astronomical data and instruments that would result in more accurate positions of planets and stars
1571 - 1630 (Johannes Kepler)
Assistant to Brahe and believed in a heliocentric system
Used sun centered system to explain all Brahe’s data
Plotted the orbits of the planets and saw that these orbits looked like flattened circles
1666 (Isaac Newton)
Falling apple made him think of the moon
Moves in circular path
Moon is accelerating because changing direction
Acceleration is caused by a force
Hypothesized that force was same force of gravity that caused an apple to fall
Moon fall should be in direct proportion to fall of apple on earth
Should relate to distances from earths center
Moons distance was 60 times greater than apple on earth. Gravity should be diluted by distance
Apple falls 4.9m in first second on earth
Moon falls 1.4mm in first second of orbit
4.9/(60)2
Fg ∝ 1/d2
Gravitational force depends on both mass of object and mass of planet
Fg ∝ m1 * m2
Hypothesized that force was proportional to the mass
Used mathematics to show that the force for elliptical paths must be inversely related to the distance squared
Showed that Force was direction along a line connecting the centers of the two bodies
So confident with his work he wrote the Universal Law of Gravity Equation
Fg = G * (m1 m2) / d2
He proved mathematically that Fg was the cause of elliptical paths of the planets by deriving Kepler’s 3rd Law from the universal gravity equation
1731 - 1810 (Henry Cavendish)
Developed a torsion balance sensitive enough to measure gravitational attraction between two masses on Earth
Gravitational constant
G = 6.67 × 10-11 Nm2/Kg2
Gravitational force is an inverse square law
Kepler’s 1st Law
Law of Ellipses
The paths of the planets are ellipses with the sun at one foci
Kepler’s 2nd Law
Law of Areas
An imaginary line from the sun to a planet sweeps out equal areas in equal time intervals.
Planets move fastest when closest to the sun, slowest when farthest away
Kepler’s 3rd Law
Law of Periods
The ratio of the squares of the periods of any two planets revolving about the sun is equal the ratio of the cubes of their average distances from the sun
Rotation
Spinning based on internal axis
Circular Motion
Spinning based on external point
Center seeking
Not centrifugal
Inertia of the object
ΣFc
Can be any type of force
Moving in a circle
384 B.C.E. - 322 B.C.E. Aristotle and Plato
Geocentric
Earth Centered
Believed the heavens were small remote objects in motion around the earth that moved with constant angular rate
310 B.C.E - 230 B.C.E (Aristarches)
Believed that the sun was the center of the universe
Heliocentric
Sun centered
Believed there were spheres for the stars, planets, and Earth
celestial sphere was motionless
earth rotates once on an axis of its own
planets moved in circular paths around the sun
150 C.E. Claudius Ptolemy
Believed both systems could be used in describing motion
Preferred geocentric theory because it fit the causes of motion of the planets, stars, and sun
Believed the earth was the center of the universe but not the center of all the heavenly circles
Ptolemy Model
Developed a very clever and rather accurate procedure for predicting the positions of each planet on a geocentric model
Constructed a model out of circles and three other geometrical devices that would each provide for variations in the rate of angular motion as seen from Earth
Eccentric
Epicycle
Equant
Successes:
Found a combination of motions that gave more accurate predictions on positions of planets to withing 2° over a long period of time
Limitation:
Not possible to calculate the period or the size of each planet’s orbit
1473 - 1543 (Nicolaus Copernicus)
Adopted the heliocentric system with the following assumptions
No precise geometrical circles
Center of the earth was not the center of the universe, but the cause of gravitation for the moon
The distance from the earth to the sun is very small in comparison to the distance to the stars
The earth has more than one motion
It rotates on an axis
It revolves around the sun
Successes (Copernicus was able to calculate):
The period of motion of each planet
The size of each planet’s orbit in comparison to the earth’s orbit
Limitations:
Founded on inaccurate data
1546 - 1601 (Tycho Brahe)
Believed in the geocentric system
Recorded positions of the planets in trying to prove the geocentric theory
Collected astronomical data and instruments that would result in more accurate positions of planets and stars
1571 - 1630 (Johannes Kepler)
Assistant to Brahe and believed in a heliocentric system
Used sun centered system to explain all Brahe’s data
Plotted the orbits of the planets and saw that these orbits looked like flattened circles
1666 (Isaac Newton)
Falling apple made him think of the moon
Moves in circular path
Moon is accelerating because changing direction
Acceleration is caused by a force
Hypothesized that force was same force of gravity that caused an apple to fall
Moon fall should be in direct proportion to fall of apple on earth
Should relate to distances from earths center
Moons distance was 60 times greater than apple on earth. Gravity should be diluted by distance
Apple falls 4.9m in first second on earth
Moon falls 1.4mm in first second of orbit
4.9/(60)2
Fg ∝ 1/d2
Gravitational force depends on both mass of object and mass of planet
Fg ∝ m1 * m2
Hypothesized that force was proportional to the mass
Used mathematics to show that the force for elliptical paths must be inversely related to the distance squared
Showed that Force was direction along a line connecting the centers of the two bodies
So confident with his work he wrote the Universal Law of Gravity Equation
Fg = G * (m1 m2) / d2
He proved mathematically that Fg was the cause of elliptical paths of the planets by deriving Kepler’s 3rd Law from the universal gravity equation
1731 - 1810 (Henry Cavendish)
Developed a torsion balance sensitive enough to measure gravitational attraction between two masses on Earth
Gravitational constant
G = 6.67 × 10-11 Nm2/Kg2
Gravitational force is an inverse square law
Kepler’s 1st Law
Law of Ellipses
The paths of the planets are ellipses with the sun at one foci
Kepler’s 2nd Law
Law of Areas
An imaginary line from the sun to a planet sweeps out equal areas in equal time intervals.
Planets move fastest when closest to the sun, slowest when farthest away
Kepler’s 3rd Law
Law of Periods
The ratio of the squares of the periods of any two planets revolving about the sun is equal the ratio of the cubes of their average distances from the sun