How to extract data beginning on the closest number to zero?

I have a list from which I want to extract only the values beginning from where b (from {a,b}) is the closest to zero. For example: I want extract data={{2, -0.036704}, {56.7499, 0.95489}, {73.7349, 0.73489}, {2, -0.237504}} from the following list: list={{1, 0.67342}, {77.7499, -0.93489},{6.73448, 0.056704},{2, -0.036704}, {56.7499, 0.95489}, {73.7349, 0.73489}, {2, -0.237504}}

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Look up Nearestin the docs. –  Yves Klett Nov 10 '13 at 18:22

One way is to find the index ind where the minimum occurs, and then take all the remaining elements of the list:
ind = First@Ordering[First@Abs[Rest[Transpose[list]]]];

For long lists, the following may be faster ind = First@ Ordering[Abs@ list[[All, 2]], 1] –  user8074 Nov 10 '13 at 19:19