The end of a pencil of mass m and length L rests in a corner as the

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The end of a pencil of mass m and length L rests in a corner as the pencil makes an angle θ with the horizontal (x) direction (Fig. P8.82). If the pencil is released, it will rotate about point O with an acceleration α1. Suppose the length of the pencil is increased by a factor of two but its mass is kept the same; the pencil would then have an angular acceleration α2when released. Find the ratio α12.

Figure P8.82

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