Question

The circular blade on a saw has a diameter of 7.25 inches and rotated at 4800 revolutions per minute.

Answer 1

Answer:

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

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