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?
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