Question

The circular blade of a saw has a diameter of 7.5 inches and rotates at 2400 revolutions per minute. a. Find the angular speed in radians per second. b. Find the linear speed of the saw teeth (in ft/s) as they contact the wood being cut.​

Answer 1

Step-by-step explanation:

Answer:

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

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

Step-by-step explanation:

step 1

Find the angular speed

we have

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

remember that

1\ rev=2\pi\ radians1 rev=2π radians

1\ min=60\ sec1 min=60 sec

substitute

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

step 2

Find the linear speed of the teeth in feet seconds

we have

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

remember that

1\ rev=\pi D1 rev=πD

1\ min=60\ sec1 min=60 sec

1\ ft=12\ in1 ft=12 in

D=7.25\ in=7.25/12\ ftD=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}4,800minrev=4,800∗(π∗7.25/12)/60=151.8secft