Answer the following angular speed questions. $($Enter your answers using exact values.$)$

$($a$)$ A wheel of radius $22$ ft$.$ is rotating $14$ RPM counterclockwise. Considering a point on the rim of the rotating wheel, what is the angular speed $$ in rad$/$sec and the linear speed v in ft$/$sec$?$

$=$

rad$/$secv $=$

ft$/$sec

$($b$)$ A wheel of radius $8$ in$.$ is rotating $15/$sec$.$ What is the linear speed v$,$ the angular speed in RPM and the angular speed in rad$/$sec$?$

v $=$

in$/$sec$=$

rpm$=$

rad$/$sec

$($c$)$ You are standing on the equator of the earth $($radius $3960$ miles$).$ What is your linear and angular speed?

v $=$

mph$=$

rad$/$hr

$($d$)$ An auto tire has radius $12$ inches. If you are driving $60$ mph$,$ what is the angular speed in rad$/$sec and the angular speed in RPM$?$

$=$

rad$/$sec$=$

rpm