Physical Science
Motion
Linear Motion
Rotational Motion
Slides subject to change
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Position
Position is the location of an object relative
to a reference point.
 Change in position is “motion.”

I am here, where
are you?
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Describe Motion

d = distance
t = time

v = d/t

Instantaneous speed
v = speed
Speedometer

Average—total
distance/total elapsed time
Odometer
Stopwatch
Motion: Drive APU to LAX
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Average Speed
Average speed equals total distance
divided by total travel time.
 Odometer reading divided by time.
 vavg = v = d/t

APU to LAX, according to Google Maps:
 d = 41.2 mi
 t = 44 min = 0.73 hr
 v = d/t = (41.2 mi)/(0.73 hr) = 56 mi/hr

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Speed or Velocity?

Speed is a scalar (a magnitude, e.g., 45
mi/hr). Speedometer reading.

Velocity has both magnitude and direction.
Average velocity is straight-line distance
between the starting point and ending
point, with an angle or “heading.” An
example would be an airplane that has
both speed and heading.
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Average Velocity
Straight-line distance between APU and
LAX is 32.7 mi (as the crow flies, called
“displacement”).
 Suppose a helicopter can do it in 20
minutes? What is average velocity?
 displacement d = 32.7 miles
 elapsed time t = 20 min = 0.33 hr
 vavg = (32.7 mi) /(0.33 hr) = 98 mi/hr
 General heading: 240° (in aviation terms,
or southwestward.

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Compass Headings
The Average Speed Formula
From the basic definition of average speed
v,
 v = d/t
 If you know the average speed v and time
t, rearrange it and you can calculate the
distance.
 d = vt
 If you know the distance d and speed v
you can calculate the time t.
 t = d/v
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
Running Track
Inside lane of a running track is usually
400 meters long. It’s the longest common
sprint race.
 Michael Johnson holds record run in 43.2
seconds. (note top speed in 2012
Olympics 43.94 s)
 What was Johnson’s average speed?
 d = 400 m
 t = 43.2 s
 v = d/t = 400/43.2 = 9.26 m/s
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
Average Speed Example
Hillary drives from Azusa to Barstow to
Needles, CA.
 Average speed Azusa to Barstow 45 mi/hr,
and it’s 60 miles.
 Average speed Barstow to Needles 75
mi/hr, and it’s 175 miles.


What’s her average
speed for the entire trip?
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Average Speed
Hillary’s average speed for the entire trip.
 v = dtot /ttot
 Divide trip into two legs.
 What’s her total distance dtot?
 Leg 1: 60 mi
 Leg 2: 175 mi
 dtot = d1 + d2 = 60 + 175 = 235 miles

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Average Speed
What’s the total time ttot?
 Leg 1: Azusa to Barstow,
 v1 = d1/t1 or rearranged, t1 = d1/v1
 or t1 = 60/45 = 1.33 hrs

Leg 2: Barstow to Needles,
 t2 = d2/v2 = 175/75 = 2.33 hrs
 ttot = t1 + t2 = 3.66 hr
 Overall v = dtot /ttot = (235)/(3.66) = 64 mi/hr

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Johnson Runs 400-m Track

What is his average velocity?
 Displacement d between start and
finish = 0
 Time t = 43.2 seconds
 velocityavg = d/t = (0)/(43.2) = 0 m/s !!

Seems strange, but it’s based on the
definition of “velocity.”
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Acceleration
Acceleration results from a change in
speed or a change in direction.
 Average linear acceleration equals change
in speed divided by the time for the
change to occur.
 aavg = (v – v0)/t

v – v0 = change in speed, i.e., final speed
minus initial speed.
 t = elapsed time

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Acceleration
a = (v – v0)/t
 If acceleration a is constant:
 Every second, the velocity is
changing by the same amount.
 Can predict future speed by
rearranging:
a = (v – v0)/t
• v is final speed
at = v – v0
• v0 initial speed
v = v0 + at
• t is elapsed time

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Top Fuel Dragster
Distance: 0.25 miles (“quarter mile”)
 Elapsed time t = 4.5 seconds
A race …
 Initial speed v0 = 0 mi/hr
 Final speed v = 330 mi/hr

If Constant Acceleration
Given
 v0 = 0 m/s
 v = 330 mi/hr = 148 m/s
 t = 4.5 second
 148 = 0 + 4.5a
 a = 33 m/s2

Formula
 v = v0 + at
Every second, it’s going 33 m/s faster.
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Compare to Earth Forces

Top fuel dragster a = 33 m/s2

An object falls in Earth’s gravity at 9.8 m/s2.
The dragster is accelerating at a rate 3.4
times faster down the track than it would
fall.
 Driver feels this as a force of 3.4 g’s on his
or her back.

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A Real Stock Race Car
Acceleration from
moment to moment
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Kingda Ka
Six Flags, Jackson, NJ
0 to 128 mi/hr in 3.5 s
Free Fall
Assume no air resistance.
 Assume acceleration is constant over
Earth surface.

a = g = 9.8 m/s2


Drop something, velocity
downward is
v = v0 + at, and a = g

Every second, an object in free fall
is going 9.8 m/s faster.
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Distance

Formula for the distance an object falls
(assume it starts from rest, and ignore air
friction), with constant acceleration, is
d = ½ at2
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Distance
Drop something, and it falls 2.0 meters.
How long does it take?
 Given
Formula
 a = g = 9.8 m/s2
 d = ½ gt2
 d = 2.0 m

2.0 = ½ (9.8)(t2)
 then, t2 = 0.408, and t = 0.64 s

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Example
Boy walks off 10-meter diving board to do
a “cannonball.”
 How long before he hits the water?
Given
Formula
d = 10 m
d = ½ gt2
g = 9.8 m/s2


d = 10 = ½ gt2 = ½ (9.8)(t2)
t = 1.4 s
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Example
Boy walks off 10-meter diving board to do
a “cannonball.”
 How fast is he going when he hits the
water?
Given
Formula
a = 9.8 m/s2
a = v/t, or v = at
t = 1.4 s

v = (9.8)(1.4) = 13.7 m/s
≈ 30 mi/hr
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Zepplins
In 1937, Hindenburg captains had a
standard way of checking their altimeters.
 Over the ocean they would periodically
drop a soda bottle and measure how long
it took to hit the water.

Suppose t = 8.0 seconds.
How high was the air ship,
in meters?
 d = ½ gt2 = ½ (9.8)(8.0)2
= 314 meters

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Projectile Motion
Projectile motion problems are best solved
by treating horizontal and vertical motion
independently.
 Gravity only affects vertical motion.


Important
 Assume no air resistance.
 Horizontal velocity is constant.
 Time in flight is the same for both
horizontal and vertical.
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Baseball
If you drop an object from 1.5 m, when will
hit the ground?
 d = 1.5 = ½ gt2 = ½ (9.8)(t2)
 t = 0.55 s.

If you throw a baseball horizontally from
height 1.5 m it will also take exactly 0.55 s
to hit the ground.
 If you fire a bullet exactly level from height
1.5 m it will also take exactly 0.55 s to hit
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the level ground.

Acceleration Same for All?
Do objects of different mass really
accelerate at the same rate?
 In an atmosphere, object experiences
“drag” from air friction and reaches a
“terminal velocity” –no more acceleration.


Thus, in an atmosphere,
size and mass matter!

No air: .
Demonstration on the Moon
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Circular Motion
Even when traveling at constant speed, an
object in uniform circular motion must have
an inward acceleration.
 Change in velocity (the direction of motion).
 When object moves in a circle of radius R
with constant speed v, centripetal
acceleration ac equals


ac = v2
R
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Constant Speed
T = period, time to go around once, the
period of revolution.
 v = distance/time = 2πR/T


A yo-yo does a “round-the-world” in 1.1 s.
The yo-yo is 0.80 meters long. What is ac?
v = d/t = 2πR/T = 2π(0.8)/1.1 = 4.57 m/s
ac = v2/R = (4.57)2/0.80 = 26 m/s2
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Centripetal Motion
• Eurofighter Typhoon centripetal acceleration reaches up to 15 g (150 m/s2). The
aircraft can increase its maximum turn acceleration in less than one second.35
Circular Motion in Jet Fighter
2-3 g’s: Pilot feels heavy.
 4 g’s: Vision switches to black and white
(gray-out).
 5-6 g’s: Oxygen to head stops completely.
G-LOC (loss of consciousness).

If g onset > 5 g /s, blackouts can happen
instantaneously and without warning.
 Takes about 30 seconds for a pilot to act
and regain his orientation.

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Anti-G Suits

The pneumatic "anti-g suit"—
five interconnected air
chambers cover the lower
abdomen, thighs, and lower
leg.

If aircraft accelerates between
1.5 to 2.0 g’s the trousers
automatically inflate.
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Maximum g’s?
No more than 9 g’s for few minutes probable blood vessel damage.
 For very short duration, very high
accelerations can be supported, although
some damage can result.
 Col. John Stapp (1910-1999), flight
surgeon, USAF, did several experiments,
strapping himself to a rocket sled, and
determined that 32 g’s was an
acceleration “someone could walk away
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from.”

Maximum g’s

Col John Stapp video
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Maximum g’s
32 g’s became the acceleration used in
the design of fighter jet ejection seats.
 Stapp survived 43 g’s, but had eye
damage.

Stapp laid engineering groundwork for the
use of seatbelts in cars.
 First seat belt law was a federal law which
took effect on January 1, 1968 (signed by
Lyndon Johnson, Stapp was invited).

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