1. ESS 303 – Biomechanics Angular Kinematics

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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°

8. Right Hand Rule

9. 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

10. 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?