BNG-202 Biomechanics II Equation Sheet - D4LABS curreyj/BNG-202_files/Equation Sheet.pdf · BNG-202

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Text of BNG-202 Biomechanics II Equation Sheet - D4LABS curreyj/BNG-202_files/Equation Sheet.pdf · BNG-202

  • BNG-202 Biomechanics II

    Equation Sheet

    +

    Particle Kinematics

    v =ds

    dt

    a =dv

    dtads = vdv

    v

    x

    = (vi

    )x

    x = xi

    + (vi

    )x

    t

    v

    y

    = (vi

    )y

    gt

    y = yi

    + (vi

    )y

    t 12gt

    2

    v

    2y

    = (vi

    )2y

    2g(yf

    yi

    )

    v = sut = vut

    a = vut +v2

    un

    =[1 + ( dydx )

    2](3/2)

    | d2ydx2 |vA/B = vA vB~rA/B = ~rA ~rB

    ~v = rur + ru + zuz~a = (r r2)ur + (r + 2r)u + zuz

    rad = 180degrees

    Particle Kinetics: Force and Acceleration

    Fx

    = max

    Fy

    = may

    Fz

    = maz

    tan =dy

    dx

    Fn = manFt = mat

    Fb = 0

    tan =r

    dr/d

    Fr = marF = maFz = maz

    f = kN 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

    mv1 +

    Fdt = mv2

    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!2rGFt = m(aG)t = mrG

    MG = IGMO = (Mk)O

    (Mk)O = m(aG)trG + IG(Mk

    )P

    = IG

    + 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 +12t2

    !2 = !2i + 2c( 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 + V2Vg = Wy = mgh

    Ve =12ks2

    translation kinetic energy

    T =12mv2

    Rotation about a fixed axis kinetic energy

    T =12mv2G +

    12IG!

    2

    x =b

    b2 4ac

    2a

  • BNG-202 Biomechanics II

    Equation Sheet

    Area Moment of Inertia