Question

A rod 1.22 meter long rotates in a horizontal plane about a vertical axis through its center. At each end of the rod is fastened a cord 0.91 meters long. Each chord supports a weight W. Compute the speed of rotation in rev/min when the weight is inclined 30 degrees with the vertical.

Answer 1

Answer on Question #79844, Physics - Mechanics | Relativity

A rod 1.22 meter long rotates in a horizontal plane about a vertical axis through its center. At each end of the rod is fastened a cord 0.91 meters long. Each chord supports a weight W. Compute the speed of rotation in rev/min when the weight is inclined 30 degrees with the vertical.

As could be seen from the Fig.1, $r = 1.22 / 2 + 0.91 * \sin 30{}^\circ = 0.61 + 0.455 = 1.065 \, \text{m}$ .

As could be seen from the Fig.2, $a = g * \tan 30{}^\circ = 9.81 * \sqrt{(1/3)} = 5.66 \, \text{m/s}^2$ .

From $a = u^2 / r$ , $u = \sqrt{(a * r)} = 2.45 \, \text{m/s} -> 147.4 \, \text{m/min}$ .

So, rotation is $n = u / (2^{*}\pi^{*}r) = 22$ rev/min.

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