Equilibrium Two conditions Torque = r x F, in two dimensions;

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Presentation transcript:

Equilibrium Two conditions Torque = r x F, in two dimensions; Sum of forces = 0, (no linear acceleration) SF=0 Sum of torques = 0, (no angular acceleration) St=o Torque = r x F, in two dimensions; t=rFsinq

Circular Linear p188-189 q=q0 + wt + ½ at2 d=d0 + vt + ½ at2 w=w0 + at v=v0 + at w2 = w02 +2aDq v2 = v02 +2aDd a=Dw/Dt a=Dv/Dt Torque; t=Ia Force; F=ma Circular motion: p193 vt=2pr/T=wr; tangential velocity w=2p/T (rad/sec); angular velocity T is time to make one rotation or revolution, one rotation or revolution is 2p radians ac=w2r=vt2/r; centripetal acceleration toward center of rotation at=ar; tangential acceleration a=dw/dt; angular acceleration

Kinetic energy Rotational KErot = ½ Iw2 Translational KEtrans = ½ mv2 Moment of Inertia point mass I=Mr2 solid sphere I = 2/5 MR2 solid cylinder/disk I= ½ MR2 Angular Momentum L=Iw; Torque t=Ia; t=dL/dt p234 P238, 240

Equations Describe observed physical properties They do not explain why Once you properly choose an equation to solve for unknowns, the rest is MATH. Be neat and orderly Be consistent with units Beware of the calculator