Name the types of motors used in vacuum cleaners, phonographic appliances, vending machines, refrigerators, rolling mills, lathes, power factor improv

vacuum cleaners: 1 phase or3 phase induction motors depending on the capacity of motor

phonographic appliances: DC motors are used in such appliances ( Mostly Speed control ) vending machines: Stepper motors are mostly used in such application with some controlled actuators

refrigerators: Simple AC motors or Induction Motors

rolling mills: Induction Motors with gear system to have more torque

lathes: AC motors as well as Dc motors are used in lathe Machine ( varying from Machine to machine)

power factor improv: Synchronous Motors are used for improving power factor but first we have to run system on induction motor to achieve near synchronous rpm

vaccum cleaners,refregirator etc ..............
Induction motors (3ph or1ph) power factor correction (synchronous motor)