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
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
Angular Kinematics
A B C
Angular Kinematics
 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
 θ = S/R
A B C
Angular Kinematics
SA = 1.57rad * 1m
SA = 1.57m
SB = 1.57rad * 2m
SB = 3.14m
SC = 1.57rad * 3m
SC = 4.71m
A B C
90° = 1.57 radians
A B C
Angle Types
Relative: angle between segments
Absolute: describes the orientation of
an object in space
Yproximal - Ydistal
Tan θ = –––––––––––––
Xproximal - Xdistal
Femoral Angle = 63.43°
(7,9)
(5,5)
Right Hand Rule
Today’s Formulas
1 radian = 57.3 degrees
θ = S/R (remember to use radians here)
Tan θ = (Yproximal – Ydistal)/(Xproximal –
Xdistal)
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 time1 (0.05s)
was 6.5rad/s and at time2 (0.54s) was
15.87rad/s
What was the angular acceleration?