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ESS 303 – Biomechanics
Angular Kinetics
Angular Kinetics
Angular or rotary inertia (AKA
Moment of inertia): An object tends to
resist a change in angular motion, a
product of mass and radius2
Rotational velocity increases with a smaller
radius
See examples on next slides
Rotational Velocity and Radius
Rotational Velocity and Radius
Angular Kinetics Formulas
Torque: rotational force; Newton Meters
Torque = Force * Radius; T = F * r
Mechanical advantage (MA) = effort arm / resistance arm
Center of mass: [(X1 * M1) + (X2 * M2)…] / (M1
+ M2…); [(Y1 * M1) + (Y2 * M2)…] / (M1 + M2…)
Work = T * ∆θ; θ is in radians; Joules (J)
Power = (angular work / time) = (T * ω); Watts
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) = 16.1JPower = (angular work / time) = (16.1J / 0.7s)
= 23.0 Watts
Force couple
Joining Linear and Angular Worlds
Joining Linear and Angular Worlds
Tangent velocity (Vt) = r * ω; use radians
Joining Linear and Angular Worlds
Centripetal force (Fc) = (M * V2) / r
Linear & Angular Problems
Calculate tangent velocity if the radius is
25m and the angular velocity is 10°/s
10°/s = 0.17rad/s
Vt = (r * ω) = (25m * 0.17rad/s) =
4.25m/s