Review cheat sheet uoft

(1)

Particle

kinematics?

Kinetics

Carviline

^NormTan

Impulse

^-^Momentum Miscellaneous

T⁼i⁼i

-=

_mv At ⁼^0.3048m

Core Formulas

G

>

a ⁼

2

^v

⁼ Rectangular ⁹²

⁼

9,

⁺

Fdt

^qus ⁼^32.2 ^ft/s2

Sp

⁼^Sot ^Vot⁺ Iat ^I⁼^xi ⁺

yy ner ^Haute ^ener

^H^-

=IqCO

^Impulse

wired

·N - Sec

Relative Motion *

I⁼x4 ⁺y)Â â⁼iei ⁺vien Î =Ex

mi

558

↑

- - - ^x

Ang Velocity

#A

⁼

FB

⁺

FAI

-

a⁼_x4 ⁺

jj

torm

^sin

ⁱⁿ ⁱ ^danus ⁱⁿ ^the

SVdt ^I

^where

^I

⁼^Four^or^a

Circular

Motions_O

actex=

^-¹⁺^x2

Non-Uniform

Acceleration

o

^an⁼^r0⁼^r0⁼⁼

^j Sa

⁼

(iron) et en ⁼ ^Exma

⁼^E

^Mo ^⑰

^small^Oe

^(since ⁱⁿ

S

⁼^Sot ^rot

+/ Y"alt" ^dt'dt'

_at⁼

_I

⁼_r0 ₀=

dine

¹

Fl

⁼^rmv= ^mr2w

d

VF⁼^Vot

15 ^act')

^dt' ^*

^er

^=-ên ârc⁼Ôr

_a

a⁼acs) ^-> ^rdw- ads

Ai= _I=

v8e+ ie (10)

₌

(H),

⁺

uodT

⁼

^I ^e

ris)-

^{a(s) ds} ^Friction ^work's

Energy ^Tr= _loco

^Remindus

a ⁼

a(r) IFfs) IMsNI

^work! ^dU⁼

^E.

^di

Vg

⁼

mg

↳_Read

Carefully

=Fdr as O ^↳^Visualize

I: "dt=

^t

^[VIt3 ^Iffx)

⁼

^(MN) ^T

⁼

^2m2 ^Vs

⁼

^bx2 ^↳ ^List^Equs

UAI=

1, ^Efu

^ds ^↳ ^Havefun

((t')

^dt⁼^1s ⁼

^s(t)

^N⁼

_my

^nos ^O

Coefficient

^of Restitution e ⁼

-Cut the

Rigid Body

^Kinematics Instantaneous Center

Rigid Body

^Kinetics

^Rigid

^-^Body

Diagram

General

Formulas

General

Plane Motion AA Y

=

^wxr

as

--

werent

_BIAA

aro

^IF⁼^maa ^[Ma⁼^Iq ^-

=woren Farnet -

^Io⁼^Ig⁺^md2 ^B

^can ^see ^it

=I

^T ⁼

^ImY,+ ^Iqw2

=

wXY

⁺

x

^T ⁼

^E

^IIcW2

dw⁼x

dO

^wheels

G

⁼

_mr, F,

⁼

IqWA

E

or⁼

= ^WX ^it. For indo Damped

Oscillation Base Excitation

i

=MSO I⁼

Emin

Absolute

Motion

Analysis

^Relative ^Motion

Analysis

^x, ⁼

^wn(-3

⁺

^VEE1)

Xi

sin an _amplitude

① Locate Pointon

body ①

^Kinematic

Diagram

¹²

=

Wn(-5-1) Undamped

^BE

②Define ^s⁼f(0)

(geometry) ②

Cross

product, equate;

^Y ⁺² ^[Wnx ⁺^Wi⁼^{0 A} ⁱ ⁺^wix ⁼

Ei(t

③ _Apply

derivatives

③

^Solve. _X ⁼

A,e

^x,t⁺^Aze^Azt Xp ⁼Xsin(rt)

Amplitude

Vibrations? Time Response Frequency:

^Wavelength^A,

^to

reponses-

F

2π

Undamped

Oscillation ^ONE

Id⁼ ^2π

Des +wnx

⁼0,

an e

fr=

E,

⁼ⁱⁿ

A=

ie ^Xp

⁼

^Fes

^sin(art)

-

-H

Wa

overdamped

^Static ^Deflection

X,

⁼^A^cos

(Wut)

⁺Bsin

(Wnt)

331,

^X,,^X2^Distinct

^So

^T ⁼

E,

⁼ ^-

X2⁼^Csin(Wnt ⁺

4)

d SsT

A:

Csin4

^B:^Cros4 ^C:

VEB2 Critically ^Damped

Magnification Amplitude

3⁼1 x,⁼Yz ^M

=

E

⁼

FTE)

Yo

⁼Brn=Ccos4Wn Vibration of

Particles =1:

^M^- ⁰

(Resonance

4=arctan

(E)

_x ⁺2wnx ⁺w ⁼

wt)

^Reaches

Equilibrium

^fastest

Underdemped

^DNF-

C-wnVI-5:

Rotation of

Rigid

^Bodies ^Fo's^Driving ^I^{<1, WdI}

wn=

^Frequency X⁼csin

(Wat +4) e'eWnt

0 ⁺

wO

⁼0

o

(2)

Mass Moments _of Inertia

Cylinder

^Thin ^Plate ^z

Ig

⁼

m

^{- >} ^radius of gyration

Ix

⁼

Emr2 Iy,

^z⁼⁼

m(2

⁺

3r2) ^Pr

^X ^Ix⁼^72m(b⁺^hz) ^a ^Go ³

Iy⁼^iz ^me ^hW ⁷ ^X

Solid

Sphere

^Z Slender Rod ^C ^z Thin Disk ^Iz

=Emb2 ^-b

I ab ^z

Ix,y,

^z ⁼

Emr2 ^a. Iy,z

⁼

Fm2 -"X ^Ix

⁼⁼^mr2

·

^Brick er

Ix⁼12m ^↑ y

In,

^z ⁼

7mr2 Is it e *a

^X

& Determine Values of ^a forwhich ②

a) 3⁼0.5

m⁼500Ky b) I⁼1.5

" "atoos. e

③

at

^barten^en

at line in

·

the C

~

reai-1200

kb,^where

an atte

_{Sin X}=

I

?

(um] RYA

I

_Assumption _of _X=_bsin(t) ^bedisplacent ic

ecim-s--

^amplitude ^cic ^cos(X-90)

SFx ⁼mi=^-ux-2cx ^wewant:0⁺

2zWnO+

^wiO⁼⁰

⑩ ^{- b - e}

[MB⁼IBx ⁼(Iq⁺^md")^x

i(mxtw*x

(Fqt

^md")^a⁼ ^ky1COSO(a) ⁺^cyccos0(^2a) ^·⁹

-

20 =

2 ZV

were ^main ^re ^intric ^nee

Î⁼^2asino ^{wa s} âÔ Îradians) êbi Î

then since

Wee

^ma ^d^YA=^a^sing ^anapproximationfor^since

E

W ^~VI ^"I>X

E ⁼_3m_V- _Velocity,so use the

jc ⁼^2a0

I

fact that Wn=^w

Ax-were at ⁽

⑤ ^d ^for ^critically ^damped so, " ⁺(CSO)⁰ ⁺(cosol⁰⁼0 ⑨^A

RI

⑥

on _and ^most

^e ^⑦ ^A

*

Ay mv,():IAW2

I

^S ^I ^mr.(B)=^(I,⁺^mra)^We

-never

^W⁼^mg ⁹³ ^x ^(l)^e ⁼^a ^Vv

^↓

^*

^*(w=

^W=^{- -}^50ton+15^mc⁺^Mv^V ^{- >}^ebf^V(z)

are

^↓

by

^0.94 ^->^0.9*s

^the ^↑

^⑫^y

^cute

^d

¹ ^e ^rar, ^e

IF⁼ma=T-mg +2⁼x²⁺n)

DTc⁼em,wh

1V⁼⁰

=strit--ex

S

·is

^Linear^Utm: ^G⁼^mYa

it list ^in. ^We

12⁺('L⁼y2 Va ⁼VB ⁺WxVa/B

i=a⁼(X2^-i2)I ^SV=-Wush I ^VA ⁼^VB ⁺^W ^X^VA/B

DTc⁺Vc+Tr^+1V⁼⁰ ¹¹⁾ _-ur

It's I 14

⁼

0 =MIV - Mrs, e

Ho=vao at ^an

⑨

, =

^↓^m²⁼^1m ^homentum^conserved⁽ ^Ho ⁼ ^2Mo

a t0=0.

X=1m ⑧

(73(0.35)kN(3310.25kg

^13(0.4)kN ^⑪ ^-^2"^-

x⁼(180^-¹²⁰⁾

EBDEE

^-

200mm - ³⁶ ⁼ ^83.5-

^- ^e ^m

=690my ^M

I

&A

I Fo^I

**, ^ie

⁽⁰⁾

^putye" to

a⁼

bot.

^E ^>3060* ^↑ ^1.625m

^↓ ↓i

^c)- - - -A

Iiz"

>40 LX ^NA ^W=^mg

↓man

^ABIA^3B

On

^Mus

^Et

⁼

^E

^AngularUtm-Imp:HAs*

EMAdt"

⁼^HAL

We fine _a

_AB⁼_GA+ _AB/A

EFx ⁼maax=

Fats

^mur=^e-^solve

I¹⁰⁰ WImg _ag⁼_dA+_A9/A ₍₀₎_-₍₁₎

⑳t

M2

N

IMA=

En egrestu ^- mgcs6o(E)

1.5mg⁼FdtFA+FB

myg ^hot ^the ^e

^⑫A⁼^Ig⁺ ^m^una

[Fy⁼⁰ ⁼^NA⁺^NB-134-mg

notrotating!

[Ma=8⁼13k(0.35)(1.625)^-NA(1.625) ⁿ⁼

1, I

[Fx⁼Ma,⁼^F,^ws60-T^{ws 30} ⁺_Ni(1.385)^-73k(0.4)(1.355)

[Fy⁼⁰ ⁼F,sin60-Tain30-mg

Review cheat sheet uoft

kinematics?

Carviline

Impulse

-=

G

2

= Rectangular 92

9,

Fdt

Sp

yy ner Haute ener

=IqCO

wired

mi

↑

Ang Velocity

#A

FB

FAI

jj

torm

in i danus in the

SVdt I

I

Circular

actex=

Non-Uniform

o

j Sa

(iron) et en = Exma

Mo ⑰

(since in

S

+/ Y"alt" dt'dt'

I

dine

Fl

15 act')

er

a

v8e+ ie (10)

(H),

uodT

I e

ris)-

Energy Tr= loco

a(r) IFfs) IMsNI

E.

Vg

mg

Carefully

I: "dt=

[VIt3 Iffx)

(MN) T

2m2 Vs

=

1, Efu

((t')

s(t)

my

Coefficient

-Cut the

Rigid Body

Rigid Body

Rigid

Diagram

General

General

=

as

werent

aro

=woren Farnet -

can see it

=I

ImY,+ Iqw2

wXY

x

E

⁼ Rectangular ⁹²

yy ner ^Haute ^ener

ⁱⁿ ⁱ ^danus ⁱⁿ ^the

SVdt ^I

^I

^j Sa

(iron) et en ⁼ ^Exma

^Mo ^⑰

^(since ⁱⁿ

+/ Y"alt" ^dt'dt'

_I

15 ^act')

^er

_a

^I ^e

Energy ^Tr= _loco

^E.

^[VIt3 ^Iffx)

^(MN) ^T

^2m2 ^Vs

⁼

1, ^Efu

^s(t)

_my

^Rigid

^can ^see ^it

^ImY,+ ^Iqw2

^E

_mr, F,

= ^WX ^it. For indo Damped

^wn(-3

^VEE1)

sin an _amplitude

③ _Apply

^to

ie ^Xp

^Fes

^So

VEB2 Critically ^Damped

3r2) ^Pr

Emr2 ^a. Iy,z

Fm2 -"X ^Ix