Answer:
Part A) The angular speed is [tex]160\pi\frac{rad}{sec}[/tex]
Part B) The linear speed is [tex]151.8\frac{ft}{sec}[/tex]
Step-by-step explanation:
step 1
Find the angular speed
we have
[tex]4,800\frac{rev}{min}[/tex]
remember that
[tex]1\ rev=2\pi\ radians[/tex]
[tex]1\ min=60\ sec[/tex]
substitute
[tex]4,800\frac{rev}{min}=4,800*(2\pi)/60=160\pi\frac{rad}{sec}[/tex]
step 2
Find the linear speed of the teeth in feet seconds
we have
[tex]4,800\frac{rev}{min}[/tex]
remember that
[tex]1\ rev=\pi D[/tex]
[tex]1\ min=60\ sec[/tex]
[tex]1\ ft=12\ in[/tex]
[tex]D=7.25\ in=7.25/12\ ft[/tex]
substitute
[tex]4,800\frac{rev}{min}=4,800*(\pi*7.25/12)/60=151.8\frac{ft}{sec}[/tex]
