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

The answer is "45.79 m/s"

Step-by-step explanation:

Given values:

diameter= 25 cm

w= 3500 rpm

Formula:

`\boxed{v=w * r} \ \ \ \ \ \ _(where) \ \ \ w = (rad)/(s) \ \ \ and \ \ \ r = meters`

Calculating r:

`r= (diameter)/(2)`

`=(25)/(2)\\\\=12.5 \ cm`

converting value into meters:
`12.5 * 10^(-2) \ \ meter`

calculating w:

`w= diameter * (2\pi)/(60)\\`

`= 3500 * (2* 3.14)/(60)\\\\= 3500 * (2* 314)/(6000)\\\\= 35 * (314)/(30)\\\\= 35 * (314)/(30)\\\\=(10990)/(30)\\\\=(1099)/(3)\\\\=366.33`

w= 366.33
`\ \ (rad)/(s)`

Calculating v:

`v= w* r\\`

`= 366.33 * 12.5 * 10^(-2)\\\\= 366.33 * 12.5 * 10^(-2)\\\\= 4579.125 * 10^(-2)\\\\\boxed{=45.79 \ \ (m)/(s)}`