Question

A 25 cm diameter circular saw blade spins at 3500 rpm. How fast would you have to push a straight hand saw to have the teeth move through the wood at the same rate as the circular saw teeth

Answer 1

Answer:

The answer is "45.79 m/s"

Explanation:

Given values:

diameter= 25 cm

w= 3500 rpm

Formula:

$\boxed{v=w \times r} \ \ \ \ \ \ _{where} \ \ \ w = \frac{rad}{s} \ \ \ and \ \ \ r = meters$

Calculating r:

$r= \frac{diameter}{2}$

  $=\frac{25}{2}\\\\=12.5 \ cm$

converting value into meters: $12.5 \times 10^{-2} \ \ meter$

calculating w:

$w= diameter \times \frac{2\pi}{60}$

   $= 3500 \times \frac{2\times 3.14}{60}\\\\= 3500 \times \frac{2\times 314}{6000}\\\\= 35 \times \frac{314}{30}\\\\= 35 \times \frac{314}{30}\\\\=\frac{10990}{30}\\\\=\frac{1099}{3}\\\\=366.33$

w= 366.33 $\ \ \frac{rad}{s}$

Calculating v:

$v= w\times r$

  $= 366.33 \times 12.5 \times 10^{-2}\\\\= 366.33 \times 12.5 \times 10^{-2}\\\\= 4579.125 \times 10^{-2}\\\\\boxed{=45.79 \ \ \frac{m}{s}}$