Answer:
Part a) [tex]120\pi\ \frac{rad}{min}[/tex]
Part b) [tex]960\pi\ \frac{in}{min}[/tex]
Step-by-step explanation:
we have
60 rev/min
Part a) Find the angular speed in radians per minute
we know that
One revolution represent 2π radians (complete circle)
so
[tex]1\ rev=2\pi \ rad[/tex]
To convert rev to rad, multiply by 2π
[tex]60\ \frac{rev}{min}=60(2\pi)=120\pi\ \frac{rad}{min}[/tex]
Part b) Find the linear speed in inches per minute
we know that
The circumference of a circle is equal to
[tex]C=2\pi r[/tex]
we have
[tex]r=8\ in[/tex] ----> given problem
substitute
[tex]C=2\pi(8)[/tex]
[tex]C=16\pi\ in[/tex]
Remember that
One revolution subtends a length equal to the circumference of the circle
so
[tex]1\ rev=16\pi\ in[/tex]
To convert rev to in, multiply by 16π
[tex]60\ \frac{rev}{min}=60(16\pi)=960\pi\ \frac{in}{min}[/tex]
