Final Formula Sheet

Final Formula Sheet - Final Formula Sheet General Rotation:...

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v=rw a t =r α a n =rw 2 Final Formula Sheet General Rotation: Angular position: θ Angular Velocity: aver: w ave = θ 2 - θ 1 /t 2 -t 1 inst: w=d /dt θ Angular Accel: aver: α ave =w 2 -w 1 /t 2 -t 1 inst: =dw/dt = d α 2 /dt θ 2 Rotation with constant (like translation w constant accel) α w=w 0 + t α = θ θ 0 + w 0 t v+ ½ t α 2 w 2 =w 0 2 + 2 ( - α θ θ 0 ) Rotation of rigid body and translation at a point on the body a= a t 2 + a n 2 = +( ) rα2 rw2 2 v b =v pA =v pB a=a tPA =a tPb Torque(unit N•m): =F• τ l = F•r•sin =F ф t •r l is perp distance from pivot to LOA Line of Action: line from F include direction: CW or CCW Special Cases: -Zero torque: LOA passes through pivot Moment of Inertia: I= r 2 dm 4 specials case that you need to know: 1) Slender rod pivoted at center: I=ML 2 /12, L is length 2) Slender rod pivoted at end: I= ML 2 /3 3) Circular disk or cylinder pivoted at the center: I=MR 2 /2 4) Point of mass M of negligible size: I=Mr2, r=distance from the pivot to particle Parallel axis theorem: I 0 =I cm + md 2 , d= distance between pivot pt and cm (cm is geometric center) I= I i (inertia of multiple is sum of indiv. inertia) Conservation ANGULAR MOMENTUM : L i =L f L=Iw so I 0 w 0 =I f w f
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Newton’s 2 nd Law for Rotation: ∑τ O = I O , O is fixed pivot, rotation center α INCLUDE DIRECTION Common problem: Mass on cable/pulley (w/ friction and tension): Two block problem(w/ no friction):
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Final Formula Sheet - Final Formula Sheet General Rotation:...

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