BNG-202 Biomechanics II Equation Sheetorzo.union.edu/~curreyj/BME-202_files/Equation Sheet.pdf ·...

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BNG-202 Biomechanics II Equation Sheet + Particle Kinematics v = ds dt a = dv dt ads = vdv v x =(v i ) x x = x i +(v i ) x t v y =(v i ) y - gt y = y i +(v i ) y t - 1 2 gt 2 v 2 y =(v i ) 2 y - 2g(y f - y i ) v s ˆ u t = v ˆ u t a v ˆ u t + v 2 ρ ˆ u n ρ = [1 + ( dy dx ) 2 ] (3/2) | d 2 y dx 2 | v A/B = v A - v B ~ r A/B = ~ r A - ~ r B ~ v r ˆ u r + r ˙ ˆ u z ˆ u z ~ a = (¨ r - r ˙ 2 u r +(r ¨ +2˙ r ˙ u z ˆ u z rad = 180degrees Particle Kinetics: Force and Acceleration F x = ma x F y = ma y F z = ma z tanθ = dy dx F n = ma n F t = ma t F b =0 tan = r dr/dθ F r = ma r F = ma F z = ma z f = μ k N F = ks Particle Kinetics: Work and Energy T 1 + V 1 + U 12 = T 2 + V 2 T = 1 2 mv 2 V g = ±Wy = ±mgh V e = 1 2 ks 2 U 12 = Z 2 1 F ds mv 1 = mv 2 e = [(v B ) 2 - (v A ) 2 ] [(v A ) 1 - (v B ) 1 ] Particle Kinetics: Impulse and Momentum m v 1 + F dt = m v 2 Line of Impact (LI) Plane of Contact (PC) (v A PC ) 1 =(v A PC ) 2 (v B PC ) 1 =(v B PC ) 2 m(v LI ) 1 = m(v LI ) 2 e = [(v B LI ) 2 - (v A LI ) 2 ] [(v A LI ) 1 - (v B LI ) 1 ] * * * These are equations you use for object hitting a wall, ground, table top etc.

Transcript of BNG-202 Biomechanics II Equation Sheetorzo.union.edu/~curreyj/BME-202_files/Equation Sheet.pdf ·...

Page 1: BNG-202 Biomechanics II Equation Sheetorzo.union.edu/~curreyj/BME-202_files/Equation Sheet.pdf · BNG-202 Biomechanics II!Equation Sheet + Particle Kinematics v = ds dt a = dv dt

BNG-202 Biomechanics II Equation Sheet

+

Particle Kinematics

v =ds

dt

a =dv

dtads = vdv

v

x

= (vi

)x

x = x

i

+ (vi

)x

t

v

y

= (vi

)y

� gt

y = y

i

+ (vi

)y

t� 12gt

2

v

2y

= (vi

)2y

� 2g(yf

� y

i

)

⌃v = sut = vut

⌃a = vut +v2

�un

� =[1 + ( dy

dx )2](3/2)

| d2ydx2 |

⇥vA/B = ⇥vA � ⇥vB

~rA/B = ~rA � ~rB

~v = rur + r✓u✓ + zuz

~a = (r � r✓2)ur + (r✓ + 2r✓)u✓ + zuz

⇡rad = 180degrees

Particle Kinetics: Force and Acceleration

⌃Fx

= max

⌃Fy

= may

⌃Fz

= maz

tan� =dy

dx

⌃Fn = man

⌃Ft = mat

⌃Fb = 0

tan⇥ =r

dr/d�

⌃Fr = mar

⌃F✓ = ma✓

⌃Fz = maz

f = µkN F = ks

Particle Kinetics: Work and Energy

T1 + V1 + ⌃U12 = T2 + V2

T =12mv2

Vg = ±Wy = ±mgh

Ve =12ks2

U12 =Z 2

1Fds

⌃mv1 = ⌃mv2

e =[(vB)2 � (vA)2][(vA)1 � (vB)1]

Particle Kinetics: Impulse and Momentum

m⌃v1 +� ⇥

⌃Fdt = m⌃v2

Line of Impact (LI) Plane of Contact (PC)

(vAP C )1 = (vAP C )2(vBP C )1 = (vBP C )2

⌃m(vLI)1 = ⌃m(vLI)2

e =[(vBLI )2 � (vALI )2][(vALI )1 � (vBLI )1]*

** These are equations you use for object

hitting a wall, ground, table top etc.

Page 2: BNG-202 Biomechanics II Equation Sheetorzo.union.edu/~curreyj/BME-202_files/Equation Sheet.pdf · BNG-202 Biomechanics II!Equation Sheet + Particle Kinematics v = ds dt a = dv dt

BNG-202 Biomechanics II Equation Sheet

Rigid Body Kinetics: Force and Acceleration

Rotation about a fixed axis

⌃Fn = m(aG)n = m!2rG

⌃Ft = m(aG)t = m↵rG

⌃MG = IG↵

⌃MO = ⌃(Mk)O

⌃(Mk)O = m(aG)trG + IG↵⌃(Mk

)P

= I

G

↵ + xm(~aG

)y

� ym(~aG

)x

Rectangular Translation

⌃Fx

= m(aG

)x

⌃Fy

= m(aG

)y

⌃MG

= IG

⌃MP

= ⌃(Mk

)P

I = Ig + md2

I = mk2

! = !i + ↵ct

✓ = ✓i + !it +12↵t2

!2 = !2i + 2↵c(✓ � ✓i)

Rigid Body Kinematics

Translation

~rA/B = ~rB � ~rA

~vB = ~vA

~aB = ~aA

Rotation

! =d✓

dt

↵ =d!

dt

=d✓

2

dt

↵d✓ = !d!

ds = rd✓

v = !r

~v = ~!x~r

~a = ↵rut + !

2run

~a = (↵xr)� (!2r)

~vB = ~vA + ~!x~rBA

~aB = ~aA + ~↵x~rBA� !

2~rB

A

Relative Motion Analysis

Rigid Body Kinetics: Work and Energy

T1 + V1 + ⌃U12 = T2 + V2

Vg = ±Wy = ±mgh

Ve =12ks2

translation kinetic energy

T =12mv2

Rotation about a fixed axis kinetic energy

T =12mv2

G +12IG!2

x =�b±

⇤b2 � 4ac

2a

Page 3: BNG-202 Biomechanics II Equation Sheetorzo.union.edu/~curreyj/BME-202_files/Equation Sheet.pdf · BNG-202 Biomechanics II!Equation Sheet + Particle Kinematics v = ds dt a = dv dt

BNG-202 Biomechanics II Equation Sheet

Area Moment of Inertia