Circular Motion and Gravitation Summary Sheet

Chapter 5

Horizontal Circle:

Mass on String

ΣFc = mac

FT = mac

Newton’s Law of Universal Grav itation

“Every particle in the universe attracts every

other particle with a force that is proportional

to the product of their masses and inversely

proportional to the square of the distance

between them. This force acts along the line

joining the two par ticles.”

Equation Result ing from Law of Universal Grav itation

GF =

G = 6.67 x 10-11 Nm2/kg2

r is the center to center distance.

Planetary Motion – Kepler’s Laws

1st law: “The path of each planet about the Sun is an ellipse with the Sun at one focus .”

2nd law: “Each plane t moves so that an imaginary line drawn from the Sun to the planet sweeps out equal

areas in equal periods of time.”

3rd law: The ratio o f the squares of the periods (the time needed for one revolution about the Sun) of any

two planets revolving about the Sun is equal to the ratio of the cubes of their mean distances from

the Sun.

Or in equation for m:

Note: use this equation to compare two objec ts that orbit the

same mass. Examples : two planets that o rbit the Sun; moon s

or satellites that orbit the same planet.

Vertical Circle: Mass on String

Top

ΣFc = mac

F + mg = mac

Bottom

ΣFc = mac

F - mg = mac

Circular Motion Equations

Period

completed circles of #

timeelapsed

T =

units: seconds

Frequency

timeelapsed

completed circles of #

f =

units: 1/second or Hz

Tangential Speed

r !2

units: m/s

Centripetal Acceleration

units: m/s2

ΣFc = mac

-FN + mg = mac

If the car looses co ntact with road, FN = 0.

ΣFc = mac

FN - mg = mac

Vertical Circle: Car on Road

ΣFc = mac

FS = mac

µsFN = mac

Horizontal Circle: Car on Track

ΣFc = mac

FN + mg = mac

Vertical Circle: Inverted

Roller Coaster Cars

Other Useful Equations Derived in Class

Acceleration due to gravity

above any planet or moon:

Ga =

To find the mass of the

object being orbited:

M =

Speed of mass in orbit:

Gv =

ΣFc = mac

FG = mmac

mE am

Horizontal Circle: Moon Orbits Earth

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Circular Motion and Gravitation Summary Sheet

Chapter 5 Horizontal Circle:

Mass on String

ΣFc = mac

FT = mac (^) r m FT

Newton’s Law of Universal Gravitation

“Every particle in the universe attracts every

other particle with a force that is proportional

to the product of their masses and inversely

proportional to the square of the distance

between them. This force acts along the line

joining the two particles.”

Equation Resulting from Law of Universal Gravitation

2 1 2 G

r

m m

F = G

G = 6.67 x 10-^11 Nm^2 /kg^2

r is the center to center distance.

m 1 m 2

FG FG

r

Planetary Motion – Kepler’s Laws

1 st^ law: “The path of each planet about the Sun is an ellipse with the Sun at one focus.”

2 nd^ law: “Each planet moves so that an imaginary line drawn from the Sun to the planet sweeps out equal

areas in equal periods of time.”

3 rd^ law: The ratio of the squares of the periods (the time needed for one revolution about the Sun) of any

two planets revolving about the Sun is equal to the ratio of the cubes of their mean distances from

the Sun.

Or in equation form:

3 2 1 2 2 1

r

T

!!^ =

&^ Note: use this equation to compare two objects that orbit the

same mass. Examples: two planets that orbit the Sun; moons or satellites that orbit the same planet.

Vertical Circle: Mass on String

Top

ΣFc = mac

F + mg = mac Bottom

ΣFc = mac

F - mg = mac r m F mg m F mg

Circular Motion Equations

Period

#ofcirclescompleted T = elapsed^ time units: seconds

Frequency

elapsedtime f =#ofcircles^ completed units: 1/second or Hz

Tangential Speed

T

2! r v = units: m/s

Centripetal Acceleration

r

v

a

c =

units: m/s^2

FN

mg

ΣFc = mac

FN + mg = mac If the car looses contact with road, FN = 0.

FN

mg

ΣFc = mac

FN - mg = mac

Vertical Circle: Car on Road

FN

mg

FS

ΣFc = mac

FS = mac

μsFN = mac

Horizontal Circle: Car on Track

FN

mg

ΣFc = mac

FN + mg = mac

Vertical Circle: Inverted

Roller Coaster Cars

Other Useful Equations Derived in Class

Acceleration due to gravity

above any planet or moon:

c (^2)

r

M

a = G

To find the mass of the

object being orbited:

2 2 3

T

r

G

M =

Speed of mass in orbit:

r

M

v = G

M

m r v ac

ΣFc = mac

FG = mmac 2 m c

E m m a

r

m m

G =

2 c

E a

r

m

G =

Horizontal Circle: Moon Orbits Earth

mE mm r

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Partial preview of the text

Download Circular motion and gravitation formula sheet and more Cheat Sheet Physics in PDF only on Docsity!

Circular Motion and Gravitation Summary Sheet

Chapter 5

Horizontal Circle:

Mass on String

ΣFc = mac

Newton’s Law of Universal Gravitation

“Every particle in the universe attracts every

other particle with a force that is proportional

to the product of their masses and inversely

proportional to the square of the distance

between them. This force acts along the line

joining the two particles.”

Equation Resulting from Law of Universal Gravitation

r

m m

F = G

r is the center to center distance.

m 1 m 2

FG FG

r

Planetary Motion – Kepler’s Laws

1 st^ law: “The path of each planet about the Sun is an ellipse with the Sun at one focus.”

2 nd^ law: “Each planet moves so that an imaginary line drawn from the Sun to the planet sweeps out equal

areas in equal periods of time.”

3 rd^ law: The ratio of the squares of the periods (the time needed for one revolution about the Sun) of any

two planets revolving about the Sun is equal to the ratio of the cubes of their mean distances from

the Sun.

Or in equation form:

r

r

T

T

!!^ =

&^ Note: use this equation to compare two objects that orbit the

Vertical Circle: Mass on String

ΣFc = mac

ΣFc = mac

Circular Motion Equations

Period

Frequency

Tangential Speed

T

Centripetal Acceleration

r

v

a

c =

FN

mg

ΣFc = mac

FN

mg

ΣFc = mac

Vertical Circle: Car on Road

FN

mg

FS

ΣFc = mac

μsFN = mac

Horizontal Circle: Car on Track

FN

mg

ΣFc = mac

Vertical Circle: Inverted

Roller Coaster Cars

Other Useful Equations Derived in Class

Acceleration due to gravity

above any planet or moon:

r

M

a = G

To find the mass of the

object being orbited:

T

r