Transcript Circular Motion - Cloudfront.net

Circular Motion
Chapter 7
Centripetal Acceleration
As a car circles a
roundabout at constant
_____, is there a change
in velocity?
Yes. Even though
magnitude is constant,
the _________ is changing.
A change in velocity means
v =
What does this represent or
mean?
According to similar triangles with similar angles, then:
similarly
So
(divide by t)
and we get
ac =
Where v = tangential velocity
And
ac =
which means:
So, anytime an object moves in an arc or
full circle, it experiences ___________
_____________.
If the object speeds up or slows down
during this, then a _____________
_____________ was also experienced,
such that there is a ____ __________.

at an angle of
where  is the angle
away from at towards
the radius.
ac
at
aNett
Consider a ball being swung on a
rope.
If a mass experiences an
acceleration, then there must be a
Force in the same direction.
i.e.
F = ma
So
Fc =
Fc is called ____________ ______.
It is a rotating force that points
towards the centre.
The __________ ______ on the swinging
ball is the ________ in the rope.
Horizontal circle –
Parallel to the ground
Vertical Circle
- Perpendicular to the ground.
FR = FC =
T=
T=
w
FR = FC =
T=
Roller Coasters (Yeah !!)
At Pt.A
FC =
n=
At Pt.B
FC =
n=
n=
n=
Earth has gravity (acceleration) and a Force due to
gravity (Weight) because of it’s _____.
The Moon’s gravity is _____ that of the Earth’s. Why?
Less _____.  Force of gravity is proportional to ______.
If the Earth was smaller, but with the same ______, what
would happen to gravity?
It would __________.
 Force of gravity is inversely dependant on the ________.
i.e.
F
&
F
The Earth pulls on the Moon with a Gravitational Force, but
The Moon also pulls on the Earth with the same Force.
(evidence?)
This Gravitational Force (FG) was formulated by
Isaac Newton (1687) and calculated by:
where:
G = 6.673 x 10-11 N.m2/kg2 (Gravitational constant)
M1 = Object at the centre
(e.g. Earth)
m2 = the orbiting object, and
(e.g. Moon)
r = distance from center to centre of the objects.
There is a Gravitational Force acting on
any 2 objects that are in proximity to each
other simply because of their masses.
e.g.’s
Pool Balls
Ball 1 is experiencing 2
attractive forces.
One from ball 2 ( ) and one
from ball 3 ( ).
The Resultant Force (F) would
cause ball 1 to move in that
direction if ______ & _____
were not present.
m1 = 0.3kg (fixed)
m2 = 0.2kg
m3 = 0.1kg (fixed)
r12 = 0.25m
r23 = 0.50m
a2 = ?
F12 = Gm1m2
r122
F23 = Gm2m3
r232
FR = F12 - F23
Where between m1 and m3 should m2 be placed such that it experiences a
zero Nett Force?
So, at the Earth’s surface, a mass (m) experiences a Force =
W=
and now
FG =
Where M1 is the Earth (ME) and m & m2 is the object which can
cancel, and r is the radius of the Earth (RE),

= (6.673x10-11Nm2/kg2)(5.98x1024kg)
(6.38x106m)2
= 9.799 m/s2
What about other planets?
Use Table 7:3 to solve.
g = 9.80 m/s2 at the surface but what happens to g as you
move away from the Earth? (increases or decreases?)
g is _________ ____________ to height.
So now, r is the Earth’s radius plus the extra height,
i.e. r =
so g at any height is:
g=
*Note*
Remember that Work (W) can equal
or
or
Well, now Centripetal Force (FC) can be the result of any of the
following:
FC =
FC =
FC =
The last equation can be used to solve for the
speed of a satellite (including the Moon) going
around the Earth.(also Earth around the Sun.)
Gravitational Potential Energy
Remember that
Substituting
PE =
=
on the Grand scale!
g=
And choosing an infinite distance away as the
reference level, we get:
PE =
Escape Velocity (vesc)
Let’s consider shooting a gun straight up.
The bullet reaches a maximum ht & returns.
A higher powered rifle will cause the bullet
to go _______, but still return.
How fast would a bullet (or anything) need
to go to escape the Earth’s pull?
Initial Energy at the Earth’s surface = Final
Energy at some distance far far away!
KEi + PEi = KEf + PEf
½ mvi2 + [-GMEm/RE] = ½ mvf2 + [-GMEm/(RE+h)]
Far far away means h =  → PEf = 0
And we get
½ mvi2 – GMEm/RE = 0
And finally
vi = vesc =
Consequences for space travel &
Rocket propulsion?
and
vf = 0
Kepler’s Laws
History:
2 A.D.: ________ develops the geocentric
model for the Universe. (Earth @ centre)
1543: _______________ develops the
________________ model . (Sun @ centre)
But all believed that the planets & stars
traveled in _________ orbits.
1600’s: Kepler interprets his mentor’s
(Tycho Brahe) data and discovers that
the orbits are in fact __________.
His labourious calculations led him to his
famous 3 laws.
(Discuss ellipses & eccentricity)
Kepler’s 1st Law:
All planets move in ___________ orbits around the Sun.
The Sun is positioned at one of the ________.
The orbits are more circular
than elliptical.
Kepler’s 2nd Law:
If you draw a line from the Sun to any planet, it will sweep
equal _______ in equal ______ intervals.
The time to travel A-B is the same for C-D
 Areas ASB & CSD are equal.
What about velocity during orbit?
Time to discuss Summer/Winter?
Kepler’s 3rd Law:
Kepler noticed that there is a proportional
relationship between the ____________ of
orbit of a planet and its ____________ from
the Sun. i.e.
Using
And
We get:
T2 = 4π2 r3
GMS
= KSr3
KS = 2.97x10-19s2/m3
Applications?
Some facts to back up Kepler’s 3rd Law: