ESS 303 -- Biomechanics

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Nov 13, 2013 (3 years and 8 months ago)

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ESS 303


Biomechanics

Angular Kinematics

From Last Time


Someone kicks a football so that it travels at a
velocity of 29.7m/s at an angle of 22
°

above
the ground


What was the vertical component of velocity?


What was the horizontal component of velocity?


SOH (sin of an angle = opposite / hypotenuse)


sin 22 = Y / 29.7m/s


Y = sin 22 * 29.7m/s =
11.13m/s


CAH (cos of an angle = adjacent / hypotenuse)


cos 22 = X / 29.7m/s


X = cos 22 * 29.7m/s =
27.54m/s

Angular Kinematics


The branch of biomechanics that deals
with the description of the angular
components of motion


Uses degrees or radians to describe
position and/or movement


Degree: 360
°

in a circle


Radian: the length of 1 radius along the arc
of a circle


1 radian = 57.3 degrees

Angular Kinematics


In the drawing to
the right


A, B &
C have the same
angular
displacement or
rotation


A, B & C have
different linear
displacements

A B C

A B C

Angular Kinematics


θ = S/R


θ = angle in radians


S = displacement
along the arc


R = radius


If radius A = 1m,
radius B = 2m, radius
C = 3m and each had
a rotation of 90
°
,
what were the
displacements of
each?

A B C

A B C

Angular Kinematics


90
°

= 1.57 radians


SA = 1.57rad * 1m


SA =
1.57m


SB = 1.57rad * 2m


SB =
3.14m


SC = 1.57rad * 3m


SC =
4.71m

A B C

A B C

Angle Types


Relative:

angle between segments


Absolute:

describes the orientation of
an object in space

(7,9)

(5,5)



Y
proximal

-

Y
distal

Tan θ =
–––––––––––––



X
proximal

-

X
distal

Femoral Angle =
63.43
°

Right Hand Rule

Today’s Formulas


1 radian = 57.3 degrees



θ = S/R (remember to use radians here)


Tan θ = (Y
proximal



Y
distal
)/(X
proximal



X
distal
)


Angular speed = angular distance/time


Angular velocity (
ω
) =
∆θ / ∆t


Angular acceleration (α) = ∆ω / ∆t

Problems


A figure skater turns 6 ½ times


What was the angular distance traveled?


What was the angular displacement?


While watching a golf swing, you note
that the angular velocity at time
1

(0.05s)
was 6.5rad/s and at time
2

(0.54s) was
15.87rad/s


What was the angular acceleration?