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