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Biomechanics II Equation Cheat Sheet, Cheat Sheet of Biomechanics

Endicott CollegeBiomechanics

Equation Sheet of Biomechanics II: Particle Kinematics - Force and Acceleration, Work and Energy, Impulse and Momentum

Typology: Cheat Sheet

2019/2020

Uploaded on 11/27/2020

jeny
jeny 🇺🇸

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BNG-202 Biomechanics II!Equation Sheet
+
Particle Kinematics
v=
ds
dt
a=
dv
dt
ads =vdv
vx=(vi)x
x=xi+(vi)xt
vy=(vi)ygt
y=yi+(vi)yt
1
2gt2
v2
y=(vi)2
y2g(yfyi)
⌃v=˙sˆut=vˆut
⌃a=˙vˆut+v2
ˆun
=[1 + ( dy
dx )2](3/2)
|d2y
dx2|
⇥vA/B =⇥vA⇥vB
~rA/B =~rA~rB
~v=˙rˆur+r˙
✓ˆu✓+˙zˆuz
~a=(¨rr˙
✓2)ˆur+(r¨
✓+2˙r˙
✓)ˆu✓+¨zˆuz
⇡rad = 180degrees
Particle Kinetics: Force and Acceleration
⌃Fx=max
⌃Fy=may
⌃Fz=maz
⌃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=1
2mv2
Vg=±Wy =±mgh
Ve=1
2ks2
U12 =Z2
1
Fds
⌃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)
(vAPC)1=(vAPC)2
(vBPC)1=(vBPC)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.
pf3

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Download Biomechanics II Equation Cheat Sheet and more Cheat Sheet Biomechanics in PDF only on Docsity!

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

gt

2

v

2

y

= (v i

2

y

2 g(y f y i

⌃v = ˙s uˆ t

= v uˆ t

⌃a = ˙v uˆ t

v

2

uˆ n

[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 = ˙ruˆ r

  • r

✓uˆ ✓

  • ˙z uˆ z

~a = (¨r r

2

)ˆu r

  • (r

✓ + 2 ˙r

✓)ˆu ✓

  • ¨z uˆ z

⇡rad = 180degrees

Particle Kinetics: Force and Acceleration

⌃F

x

= ma

x

⌃F

y

= ma

y

⌃F

z

= ma

z

tan =

dy

dx

⌃F

n

= ma

n

⌃F

t

= ma

t

⌃F

b

tan ⇥ =

r

dr/d

⌃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

= ±W y = ±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 P C

) 1

= (v A P C

) 2

(v B P C

) 1

= (v B P C

) 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.

Rigid Body Kinetics: Force and Acceleration

Rotation about a fixed axis

⌃F

n

= m(a G

n

= m!

2

r G

⌃F

t

= m(a G

t

= m↵r G

⌃M

G

= I

G

⌃M

O

= ⌃(M

k

O

⌃(M

k

O

= m(a G

t

r G

+ I

G

⌃(M

k

P

= I

G

↵ + ¯xm(~a

G

y

ym¯ (~a

G

x

Rectangular Translation

⌃F

x

= m(a

G

x

⌃F

y

= m(a

G

y

⌃M

G

= I

G

⌃M

P

= ⌃(M

k

P

I = I

g

  • md

2

I = mk

2

i

c

t

i

i

t +

↵t

2

2

2

i

c

i

Rigid Body Kinematics

Translation

~r

A/B

= ~r

B

~r

A

~v

B

= ~v

A

~a

B

= ~a

A

Rotation

d✓

dt

d!

dt

d✓

2

dt

↵d✓ = !d!

ds = rd✓

v = !r

~v = ~!x~r

~a = ↵ruˆ

t

2

rˆu

n

~a = (ˆ↵xˆr) (!

2

ˆr)

~v

B

= ~v

A

+ ~!x~r B

A

~a

B

= ~a

A

+ ↵~x~r B

A

2

~r B

A

Relative Motion Analysis

Rigid Body Kinetics:

Work and Energy

T

1

+ V

1

+ ⌃U

12

= T

2

+ V

2

V

g = ±W y = ±mgh

V

e

ks

2

translation kinetic energy

T =

mv

2

Rotation about a fixed

axis kinetic energy

T =

mv

2

G

I

G

2

x =

b ±

b

2

4 ac

2 a