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.
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
Top Related