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ESS 303 – Biomechanics

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?

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ESS 303 – Biomechanics

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  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 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 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 A B C

  7. (7,9) (5,5) 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°

  8. Right Hand Rule

  9. 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

  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 time1 (0.05s) was 6.5rad/s and at time2 (0.54s) was 15.87rad/s • What was the angular acceleration?

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