other 2d motion periodic motion: shm and ucm what’s with all these letters?

Other 2D Motion

Periodic Motion: SHM and UCMwhat’s with all these letters?

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?

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?

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

Uniform Circular Motion

UCM the motion of an object at constant spd, NOT velocity, along a curved path of fixed radiusis the particle accelerating??

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

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

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

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

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)

Pendulum In Motion

•x = amp

•v = 0

•a = max

•x = amp

•v =0

•a =max

•x = 0

•v = max

•a = 0

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