Motion or rigid body: translation + rotation KE= ½mv 2 cm + ½I cm ϖ 2 V cm = r ϖ Rolling w/o slipping diagram: V ground = V T + V cm U=mgy cm Σ F ext = ma cm Σ τ z = I cm α z iff axis through cm is axis of symmetry & does not change direction use 2 equations: Στ & Σ F for same body W = ∫ θ 1 θ 2 τ d θ For constant torque: W= τ ( θ 2- θ 1 ) W tot = ½I ϖ 2 2 – ½I ϖ 1 2 Power: P = τϖ Angular Momentum: L=r x p = r x mv = mvl dA/dt = r x F = τ the rate of change of a particle = the torque of the net force acting on it L = I ϖ-- L & ϖ have same direction Στ = dL/dt when net external force = 0, total angular momentum is constant Precession angular speed: Ω = τ /L = rmg / I ϖ Conditions for equilibrium: 1. Σ F ext = 0 & 2. Στ = 0 static equilibrium: no translational/ rotational motion center of gravity=center of mass if g has the same value at all points higher the cm, smaller incline needed to tip Elastic Modulus : stress/strain Tensile stress: F/A Tensile
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This note was uploaded on 10/06/2008 for the course PHYSICS 140 taught by Professor Evrard during the Spring '07 term at University of Michigan.