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Physical SciencePhysical Science
MotionMotionLinear MotionLinear Motion
Rotational MotionRotational Motion
Slides subject to changeSlides 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?
Describe Motion
Average—total distance/total elapsed time
d = distance t = time v = speed
v = d/t
Instantaneous speedSpeedometer
Odometer
Stopwatch
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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.
Compass Headings
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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 What’s her average speed for the speed for the entire tripentire 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
at = v – v0
v = v0 + at
• v is final speed• v0 initial speed• t is elapsed time
Top Fuel Dragster
Distance: 0.25 miles (“quarter mile”) Elapsed time t = 4.5 seconds Initial speed v0 = 0 mi/hr Final speed v = 330 mi/hr
A race …
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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 Acceleration from moment to momentmoment to moment
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Free Fall Assume no air resistance. Assume acceleration is constant over
Earth surface. a = g = 9.8 m/s2
Drop something, Drop something, velocityvelocity downward is downward is
vv = = vv00 + + at, and a = gat, and a = g
Every second, an object in free fall Every second, an object in free fall is going 9.8 m/s faster.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 a = g = 9.8 m/s2
d = 2.0 m
2.0 = ½ (9.8)(t2) then, t2 = 0.408, and t = 0.64 s
Formula d = ½ gt2
Example
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Boy walks off 10-meter diving board to do Boy walks off 10-meter diving board to do a “cannonball.”a “cannonball.”
How long before he hits the water?How long before he hits the water?
GivenGiven FormulaFormula
d = d = 10 m10 m d = d = ½½ gt gt22
gg = 9.8 m/s = 9.8 m/s22
d = d = 10 10 = = ½½ gt gt2 2 = ½ = ½ (9.8)(9.8)(t(t22))
t t = 1.4 s= 1.4 s
Example
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Boy walks off 10-meter diving board to do Boy walks off 10-meter diving board to do a “cannonball.”a “cannonball.”
How How fastfast is he going when he hits the is he going when he hits the water?water?
GivenGiven FormulaFormula
aa = 9.8 m/s = 9.8 m/s22 aa = = vv//t, or v = att, or v = at
t = 1.4 st = 1.4 s
v = (v = (9.8)(1.4) = 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 Suppose tt = 8.0 seconds. = 8.0 seconds. How high was the air ship, How high was the air ship, in meters?in meters?
dd = ½ = ½ gtgt22 = ½ (9.8)(8.0) = ½ (9.8)(8.0)22 = 314 meters = 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 the level ground.
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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, Thus, in an atmosphere, size and masssize and mass matter! matter!
No air: .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. A yo-yo does a “round-the-world” in 1.1 s. The yo-yo is 0.80 meters long. What is The yo-yo is 0.80 meters long. What is aacc??
vv = d/t = 2 = d/t = 2ππR/TR/T = = 22ππ(0.8)/1.1 = 4.57 m/s(0.8)/1.1 = 4.57 m/s
aacc = = vv22//R = R = (4.57)(4.57)22/0.80 = 26 m/s/0.80 = 26 m/s22
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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.
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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 from.”
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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).
