Question

1. A small bead is free to slide without friction on a rotating wire. The angular speed of the wire is w. In the coordinate system that rotates with the wire, there will be fictitious Coriolis and centrifugal forces, in addition to the real normal force the wire exerts on the bead. Working in this rotating coordinate system, (a) Draw the force diagram, including the fictitious forces. Write down the F=ma equations for the directions parallel and perpendicular to the wire. (Ignore gravity.) (b) Solve the parallel equation to find an expression for r(t), the distance of the bead from the rotation axis as a function of time. As initial conditions, take: r(0) 1 m, (0) = 0. (c) Find the magnitude of the normal force as a function of time, assuming the same initial conditions.

Answer 1

(a) In a coordinate system rotating with the wire, the motion is burely radial Frant Tentrifugal force & Fant. For cosolis force Front a mi N-forzo (6): Fant zmwr mä-mwer zo. r = A 6 Wt + Be wt). (C) Ne for - 2mÅw 22 mw? (A at Be wt, For r(O)= lm, ((0)=0 IN= 2mw²coshut Griven rozim, i(0)zo ra IX coshut recoshut