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Are you registered to vote in Colorado, or interested in getting registered?
(Deadline is October 3 to register) The election this year is "off-cycle", but that
doesn't mean you should ignore it. There are ballot issues this year that can (and will) directly
impact you, and I encourage you toGet informed, and choose to vote!
• 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
r
varadial
2
r
T
r2
2
2
24
T
r
27
112
)10155.3(
)105.1(4
s
maradial
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
sm
gsmaradial
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||
r
mmGF 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||
r
mmGF gravity
How Strong is Gravity?
r = 1 meter
m1 = 70 kg m2 = 70 kg
221||
r
mmGF gravity
22
211
1
70701067.6
m
kgkg
kg
Nm
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 = Both
Person #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
R
mMGF
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:
