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Chapter 11 Rolling, Torque, and Angular Momentum Section 11.2 & 11.3 Rolling as Translation and Rotation Combined & Kinetic Energy of Rolling Vcm = ωr K = ½ Iω2 Combining the rotational and translational kinetic energy to get total kinetic energy we get: K = ½ mv2 + ½ Iω2 Section 11.4 The Forces of Rolling Friction and Rolling Remember acm = αr So a tangential frictional force will slow a rotational object according to the equation: macm = mαr Section 11.7 & 11.9 Angular Momentum & Rigid Bodies Linear Momentum – the product of Mass and Velocity. ρ = mv Angular Momentum (l) – the product of Rotational Inertia and Angular Velocity. L = r x ρ = m(r x v) L = Iω The Relationship between Linear and Angular Momentum Linear momentum = ρ Angular momentum = L L = ρxr where r is the radius of rotation. Changing of Angular Momentum (Impulse) In a linear system the change in momentum, known as impulse, was given by: FΔt = mΔV In an angular system the change in angular momentum is given by: FrΔt = IΔω or ΤΔt = IΔω Section 11.11 Conservation of Angular Momentum Just as Linear Momentum was conserved, Angular Momentum must also be conserved in a closed system. So: Iiωi = Ifωf Chapter 12 Equilibrium and Elasticity Section 12.2 & 12.3 Conditions of Equilibrium ∑Fx = zero ∑Fy = zero This is Translational ∑Fz = zero Equilibrium! ∑Text = zero This is Rotational Equilibrium! Section 12.4 Center of Gravity The gravitational force on a body, Fg, effectively acts on a single point, called the center of gravity. If Fg is the same for all elements of a body, then the body’s center of gravity is coincident with its center of mass. Section 12.5 Some Examples of Static Equilibrium Car on a Bridge A 2000 kg car rests, 50 meters from one end of a 100,000 kg uniform bridge which is 300 m long and has supports at 100 and 200 m. What force acts on each support? People on a Porch Swing Suzie (m = 50 kg) and Johnny (m = 65 kg) are sitting on either end of a 1.5 m, 80 kg uniform swing which is held up by two chains. What is the force on each chain? Section 12.7 Elasticity Tension – the stretching of an object by force (outward pull) Compression – The compacting of an object by force (inward push) Tension and Compression are at right angles to the plane of the object. Shearing – is also a stress, however it is in the plane of the area rather than at right angles to it.