A belt runs a pulley of radius 8 inches at 60 revolutions per minute. a) Find the angular speed in radians per minute. b) Find the linear speed in inches per minute.

Answer:Part a) [tex]120\pi\ \frac{rad}{min}[/tex]Part b) [tex]960\pi\ \frac{in}{min}[/tex]Step-by-step explanation:we have60 rev/minPart a) Find the angular speed in radians per minutewe know thatOne 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 minutewe know thatThe circumference of a circle is equal to[tex]C=2\pi r[/tex]we have[tex]r=8\ in[/tex] ----> given problemsubstitute[tex]C=2\pi(8)[/tex][tex]C=16\pi\ in[/tex]Remember thatOne revolution subtends a length equal to the circumference of the circleso[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]