An old record is spinning on an equally old turntable at $78$ rpm $($revolutions per minute$).$ Answer all of the questions below in MKS units. $($a$)$ How many times does the record rotate per second? $($b$)$ What is the angular frequency of the record? $($c$)$ How long does it take the record to complete one revolution? $($d$)$ What is the speed of a dust particle stuck to the record at a point which is $4$ inches from the record$$s axis of rotation? $($e$)$ What is the centripetal acceleration of the dust particle mentioned above?