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This is from an example in a book:
On a horizontal turntable that is rotating at constant angular speed, a bug is crawling outward on a radial line such that its distance from the center increases quadratically r=bt^2, \theta=\omegat where b, \omega are constants. The example then solves for the acceleration of the bug (using r, \theta unit vectors)
dr/dt = 2bt; d^2r/dt^2 = 2b; d\theta/dt = \omega; d^2\omega/dt^2=0
So
a=e_r(2b-bt^2\omega^2) + e_{\theta}(0 + 2(2bt)\omega)
=b(2-t^2\omega^2)e_r + (4bt\omega)e_{\theta}
So as t goes to infinity, the acceleration in the radial component becomes negative. But the velocity in the radial direction is just 2bt, which increases with time.
How does this work (the book just says to note the radial acceleration is negative )?
On a horizontal turntable that is rotating at constant angular speed, a bug is crawling outward on a radial line such that its distance from the center increases quadratically r=bt^2, \theta=\omegat where b, \omega are constants. The example then solves for the acceleration of the bug (using r, \theta unit vectors)
dr/dt = 2bt; d^2r/dt^2 = 2b; d\theta/dt = \omega; d^2\omega/dt^2=0
So
a=e_r(2b-bt^2\omega^2) + e_{\theta}(0 + 2(2bt)\omega)
=b(2-t^2\omega^2)e_r + (4bt\omega)e_{\theta}
So as t goes to infinity, the acceleration in the radial component becomes negative. But the velocity in the radial direction is just 2bt, which increases with time.
How does this work (the book just says to note the radial acceleration is negative )?