Mathematics: The circular blade on a saw has a diameter of 7.25 inches and rotated at 4800 revolutions per minute. a)find the angular speed of the blade in radians per second. b) find the linear speed of the teeth in feet seconds as they contact the wood being cut.

The circular blade on a saw has a diameter of - id7254844347, kendricklamar29

briannaandmakayla33

17.01.2022

Part A) The angular speed is $160\pi\frac{rad}{sec}$

Part B) The linear speed is $151.8\frac{ft}{sec}$

Step-by-step explanation:

step 1

Find the angular speed

we have

$4,800\frac{rev}{min}$

remember that

$1\ rev=2\pi\ radians$

$1\ min=60\ sec$

substitute

$4,800\frac{rev}{min}=4,800*(2\pi)/60=160\pi\frac{rad}{sec}$

step 2

Find the linear speed of the teeth in feet seconds

we have

$4,800\frac{rev}{min}$

remember that

$1\ rev=\pi D$

$1\ min=60\ sec$

$1\ ft=12\ in$

$D=7.25\ in=7.25/12\ ft$

substitute

$4,800\frac{rev}{min}=4,800*(\pi*7.25/12)/60=151.8\frac{ft}{sec}$

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