1. ESS 303 – Biomechanics Angular Kinetics

2. Angular or rotary inertia (AKA Moment of inertia): An object tends to resist a change in angular motion, a product of mass and radius 2 Rotational velocity increases with a smaller radius See examples on next slides

3. Rotational Velocity and Radius

5. Angular Kinetics Formulas Torque: rotational force; Newton Meters Torque = Force * Radius; T = F * r Mechanical advantage (MA) = effort arm / resistance arm Center of mass: [(X 1 * M 1 ) + (X 2 * M 2 )…] / (M 1 + M 2… ); [(Y 1 * M 1 ) + (Y 2 * M 2 )…] / (M 1 + M 2… ) Work = T * ∆θ; θ is in radians; Joules (J) Power = (angular work / time) = (T * ω); Watts

6. Angular Kinetics Problems Find the center of mass if point A (1,2) has a mass of 2kg, point B (2.2,3.5) has a mass of 3.5kg, and point C (4,3) has a mass of 1.25kg COM = (2.18,2.96) Calculate work and power if a torque of 35Nm cause the rotation of 0.46 radians in 0.7s. Work = (T * ∆θ) = (35Nm * 0.46rad) = 16.1J Power = (angular work / time) = (16.1J / 0.7s) = 23.0 Watts

7. Force couple Joining Linear and Angular Worlds

8. Tangent velocity (V t ) = r * ω; use radians

9. Joining Linear and Angular Worlds Centripetal force (F c ) = (M * V 2 ) / r

10. Linear & Angular Problems Calculate tangent velocity if the radius is 25m and the angular velocity is 10°/s 10°/s = 0.17rad/s V t = (r * ω) = (25m * 0.17rad/s) = 4.25m/s