A small block of mass

PHYSICS · Multi-part · Fermi University Physics · Mechanics & Dynamical Systems · Kinematics and Newtonian dynamics of particles · Kinematics and Newtonian dynamics of particles

Action and Symmetry, Ch Constraints, generalised coordinates and Lagrange's equations twice over

Problem

A small block of mass m=2.0 kgm=2.0\,\mathrm{kg}, tied to a string, moves in a horizontal circle of constant radius r=0.50 mr=0.50\,\mathrm{m} at constant angular speed ω=4.0 rad s−1\omega = 4.0\,\mathrm{rad\,s^{-1}}, so θ(t)=ωt\theta(t)=\omega t. Someone argues: "the radius doesn't change, so r¨=0\ddot r=0; Newton's second law in the radial direction is mr¨=Frm\ddot r = F_r, so Fr=0F_r=0: the string need not pull on the block at all." ((a)) Give the correct radial equation of motion in plane polar coordinates and use it to find FrF_r, the radial component of the net force on the block. ((b)) Say exactly which step in the quoted argument is wrong.

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