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Other 2D Motion
Periodic Motion: SHM and UCMwhat’s with all these letters?
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Portoflio Problems
A car is getting off the interstate. The ramp is a circle, and the posted speed limit is 45 mph. If the centripetal accleration should be .3 g, what is the minimum radius the ramp should be?
A pendulum of length 1 m is brough to planet X. The period of this simple pendulum is found to be 1.5 minutes. What is the gravity on planet X?
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College Prep Portfolio
A car is getting off the interstate where the speed limit is 65 mph. If the centripetal acceleration should .3 g and the radius of the ramp is 120 feet, how far should be allowed for the deccleration lane?
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Periodic Motion (CH 7)
type of motion in which a body is repeatedly moving over the same path in equal intervals of time
Examples:springpendulummerry-go-round??????UCM and SHM
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Uniform Circular Motion
UCM the motion of an object at constant spd, NOT velocity, along a curved path of fixed radiusis the particle accelerating??
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UCM ctd.
Period time required for one complete revolution (units of time)T = 2*pi*r/|v|
where pi = 3.14 . . . . r = radius of circlev = velocity of object Why 2*pi*r?
(Dist around circle)
Frequency inverse of periodunits of Hertz inverse sec
Angular velocity () how fast something rotates
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More UCM Displacement Vectors Same magnitude directed from center out
Velocity Vectors1. same magnitude (same
speed, same length)2. diff directions, tangent to
circle and perpendicular to displacement vector
Acceleration Vectors centripetal acceleration
“center seeking” directed in toward center always opposite of
displacement ac = v
2/r
Also:
ac=42r/T2
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Simple Harmonic Motion
Gotta keep those lovin’ good vibrations are happening with her
SHM type of motion in which a particle’s acceleration is proportional to its displacement from its equilibrium position and is always directed toward equilibrium
examplesvib tuning forkmass on stringsimple pendulum
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SHM Properties equlibrium
midpoint of path
displacementdist from equilwhat is this for UCM?
radius
amplitudemax displacement
period time for 1 complete vibration
frequency# of vibrations per unit time
Before it starts:
•x = 0
•v = 0
•a = 0
Start it off!
•x = 0 (equil)
•v = max
•a = 0•x = amplitude
•v = 0
•a = max
•x =ampl
•v =0
•a = max
ashm = 42x/T2
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Pendulum Tic Toc, Tic Toc, def = an object mounted in such a way that it
can swing back and forth about an axis Properties:
pd. is indpt of masspd is indpt of amplitude
these imply that the arc is small (less than 15o)
pd sqr(length)pd 1/sqr(g)
T = 2*sqrt(l/g)
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Pendulum In Motion
•x = amp
•v = 0
•a = max
•x = amp
•v =0
•a =max
•x = 0
•v = max
•a = 0
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Book Problems
UCMpg. 145
#10 a, 11 a (ignore references to force)
pg. 151 RC#4
pg 152 Problems#13 a, #14 a, #16
a,b,d, #17 a, #18 a,b, #19 a
SHMpg. 149
#13,14
pg. 151 RC#9, #10, #12 (ignore
force)
pg. 152 AC#10,11
pg. 152 Problems#21,22