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#### karush

##### Well-known member

- Jan 31, 2012

- 2,928

the $\displaystyle5\text { in}$ pulley is rotating at $\displaystyle\frac{1000\text{ rev}}{\text{min}}$

What is the linear $\displaystyle\text{v}$ in $\displaystyle\frac{\text{ft}}{\text{sec}}$ of the belt?

$\displaystyle \text{v}=

\frac{1000\text{rev}}{\text{min}}

\cdot\frac{\text{min}}{60\text{ sec}}

\cdot\frac{10\pi \text{ in}}{\text{rev}}

\cdot\frac{\text{ ft}}{12 \text{in}}

=\frac{125\pi\text{ ft}}{9\text{sec}}

=43.63\frac{\text{ft}}{\text{sec}}

$

How many revolutions per min is the $\text{3 in}$ pulley making?

so

$\displaystyle \omega_{3in}

=\frac{5}{3}

\cdot\frac{1000\text{rev}}{\text{min}}

\approx 1667\frac{\text{rev}}{\text{min}}$

no ans in bk on this so hope ans here is perhaps it.