Some Equations for Exam 2•For this exam, use the approximation thatg=10m/s2.•For a functionf(x)=axn, wherenis an integer,dfdx=naxn-1.•Work by±Fmoving fromitof:W=±fi±F·d±sPower:P=dWdt•Kinetic energy:K=12mv2; for rotating bodies,K=12Iω2.•Potential energy: ΔU=-±fi±F·for a conservative force; andFx=-∂U∂x, etc.•Gravitational potential energy near the Earth’s surface:U=mgh.•For an ideal spring, force:F=-kx; potential energy:U=122.•For a system,Wext=ΔEmecK+ΔU. For an isolated system,Wext= 0, soEmecis constant and ΔKU=0.•Momentum:±p=m±v;Newton’s 2ndLaw:±F=d±pdt.•For a system with Σ±Fext,tot= const.•Position of the center of mass:±rcm=1MΣmii,whereM=Σmi.•Angular velocity:ω=dφdt. Angular acceleration:α=dωdt.•For a constant angular acceleration,ω=ω0+αtandφ=φ0+ω0t+12αt2.•For circular motion, the tangential component of acceleration isat=αr; the radial(centripetal) component isar=v2/r=ω2r.•Rotational inertia, or moment of inertia:I=±r2dm.–for a solid sphere about any diameter:
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This note was uploaded on 04/30/2008 for the course PHY 317k taught by Professor Kopp during the Fall '07 term at University of Texas at Austin.