Wire with Bead


A curved wire is in the shape of r = 3θ. If a bead, point A, moves along the curve at a constant rate of dθ/dt = 8 rad/s, what is the acceleration magnitude at A? Distance units are meters.



Acceleration Vectors of Bead


The total acceleration is a combination of both the r and θ accelerations.

The r terms can be found by taking derivatives,

The θ terms are given,

Combining equations and terms give,

The total acceleration is
     a = (ar2 + aθ2)0.5 = ( -201.12 + 3842)0.5 =

v = 433.5 m/s2

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