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Announcements• CAPA Set #6 due Friday at 10 pm

• CAPA Set #7 now available, due next Friday

• Next week in Section Assignment 4: Circular Motion & Gravity

• Finish reading all sections of Chapter 5

• Advanced reminder Exam #2 on Tuesday, October 11

• Reminder about office hours … Nagle (Monday 2-3 in office, Wednesday 1:45-3:45 pm help room) Kinney (Thursday 4-5 pm help room) Uzdensky (Tuesday 11am-noon help room)

If you find a missing clicker, please bring it to me or the Main Physics Office

Circular Motion – fixed radius and at constant speed |v|

Always accelerating due to change in direction of velocity vector.

Centripetal acceleration inwards towards the circle center with magnitude |a| = v2/r

“Wall-of-Death”

But don’t I feel out outward force?

This is a “fictitious” force, not real.

Consider the “Wall-of-Death”Which diagram correctly shows the real forces on the rider?

“Centripetal force”: a real force.

Clicker Question Room Frequency BA

Fictitious force: “centrifugal force”

– in the rider’s frame.

Centrifugal force (from Latin centrum, meaning "center", and

fugere, meaning "to flee“)

1

2

3

What are the three forces #1, 2, 3?

A) 1 - gravity2 - centrifugal force3 – friction

B) 1 – friction2 – normal force of the wall3 – gravity

C) 1 - centripetal force2 – normal force of the wall3 – friction

D) 1 – friction2 – centrifugal force3 - gravity

Clicker Question Room Frequency BA

rm

Choose a coordinate system: Usually radial and tangential.

For uniform motion, velocity in the tangential direction is constant, so

Σ FT = m aT = 0

In the radial direction:

Σ FR =m aR = mv2/r

Tangential (T)

Radial (R)

Dynamics of Uniform Circular Motion

For every case of uniform circular motion, there must be a force directed towards the center.

We say there is a centripetal force. However, there is always a specific force that is acting. There is no “circle force”. Circular motion does not cause a force.

Ball circling around tied to a

string.Centripetal force Tension Force

Wall of Deathride Centripetal force Normal Force

Race Car driving in circle

Centripetal force Friction Force

Spinning Bucket of Water

The Earth circles the Sun at an average distance of 1 Astronomical Unit = 1.5 x 1011 meters in one year.

What is its orbital centripetal acceleration?

r = 1 AUE

rvaradial

2

rTr 22

2

24Tr

27

112

)10155.3()105.1(4

smaradial

2/ 006.0 smaradial Sometimes we quote accelerations relative to g (9.81 m/s2).

g of %06.00006.0/81.9

1 / 006.0 22 g

smgsmaradial

The Earth circles the Sun at an average distance of 1 AU = 1.5 x 1011 m in 1 year.

What’s causing the centripetal acceleration?

A) The electrostatic force between the Earth and Sun.

B) The tension in the string connecting the Earth to the Sun.

C) The force of gravity between the Earth and the Sun.

D) Depends on the time of day.

r = 1 AUE

τ = 365 days

Clicker Question Room Frequency BA

2/ 006.0 smaradial

Newton’s Law of Universal Gravitation

Insight: what keeps the Moon in orbit around the Earth and the Earth in orbit around the Sun

is exactly the same thing that causes an

“apple to fall from a tree”.

“Every particle in the universe attracts every

other particle.”

G 6.67 x 10 11Nm2 / kg2

“Every particle in the universe attracts every other particle with a force proportional to the product of their masses

and inversely proportional to the square of the distance between them.

The force points along the line joining the two particles.”

Newton’s Law of Universal Gravitation

221||

rmm

GF gravity

Universal Gravitation Verification

1687: Isaac Newton published Gravity Theory

1798: Henry Cavendish confirmed this formula experimentally

1915: Albert Einstein’s General Theory of Relativity explained why gravity behaves this way.

221||

rmm

GF gravity

How Strong is Gravity?

r = 1 meter

m1 = 70 kg m2 = 70 kg

221||

rmm

GF gravity

22

211

170701067.6m

kgkgkgNm

Newtons 103.3|| 7gravityF

Pounds 105.7 8

That is about 1/60th the weight of a single hair.

Who does the force act on?

r = 1 meter

m1 = 70 kg m2 = 70 kg

Newtons 103.3|| 7gravityF

Answer = BothPerson #1 exerts a force on Person #2

Person #2 exerts a force on Person #1

Objects are extended in space. Newton’s Law of Universal Gravitation is based on

computing the distance between two objects, but which distance?

RCM

Extended Objects

In fact, every part of object #1 exerts a gravitational attraction on every part of object #2, and vice versa.

When adding all vector components, we treat the force as acting between the “center of mass” of each object.

“Center of mass” for sphere = middle

Consider the force of gravity exerted by the Earth with mass ME on a person of mass m on its surface?

RE

Big G, Little g

2||E

Egravity

RmM

GF

26

242211

1037.6

1098.5/1067.6||m

kgmkgNmF gravity

2/81.9|| smmF gravity

mgF gravity||

Gravitational force on an object on the surface of the earth!

You are standing on the surface of the earth.

The earth exerts a gravitational force on you Fearth, and you exert a

gravitational force on the earth Fperson.Which of the following is correct:

A) Fearth > Fperson

B) Fearth < Fperson

C) Fearth = Fperson

D) It’s not so simple, we need more information.

Clicker Question Room Frequency BA

Newton’s Third Law