A threaded rod with 12turns/ cm and diameter 1.18cm is mounted horizontally. A bar with a threaded hole to match the rod is screwed onto the rod. The bar spins at 216rev/ min. How long will it take for the bar to move 1.50cm along the rod?
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Here, distance between two consecutive threads = pitch $=\frac{1}{12}\text{cm.}$ Total distance to be moved = 1.5m $\therefore$ No. of rotations $=\frac{1.5}{\frac{1}{12}}=18$ Total angle of turing, $\theta=18\times2\pi=36\pi$ radian angular speed, $\omega=2\pi\text{n}=2\pi\times\frac{216}{60}=7.2\pi\text{rad/s}$ $\therefore$ time taken, $\text{t}=\frac{\theta}{\omega}=\frac{36\pi}{7.2\pi}5\text{s}.$
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