PHYS 161H Lecture 2: Circular and Relative Motion Physics 161H
16 Mar 2016
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Uniform circular motion (speed is constant: a(radial)=v^(2)/r(local) = 4 pi^(2)r/ (t^2, v(radial)=2pi r/t, a(tangential)=0. Non uniform circular motion: a(radial)=v^2/r =(centripetal acceleration, a(tangential)=d|v|/dt. Unit vector tangent to the curve: v=v t where v=v(t) and t=t(t) a= v dt/dt + dv/dt t first term is a perpendicular or a radial and second term is a parallel or a tangential. At inflection points, there is no radial acceleration, just a possibility of tangential acceleration. Driving over a hill of radius r, what velocity do you have to drive over the hill to feel weightless (absence of a normal force) arad=v^2/r, given r, find minimum velocity for weightlessness. +n-mg=m(-v^2/r) weightless= no normal force so: -mg=m(-v^2/r), so v=sqrt(gr) Rock going around in a vertical circle, swing around on a string with minimum velocity needed to keep the string taut. Curved road with a radius of curvature r, what frictional force is required to make a given turn.
