I want to know how rpm affects such application. And why it has to be considered.
Depends on the application. To move a conveyor belt you need a slower RPM than to turn a fan. You pick a RPM appropriate for the application. Best I can do without more information
Machines are designed to operate at a stated speed. You select, (and gear or belt), your motor so that the desired speed is attained with the motor at its rated rpm. You size your motor so that it can maintain it's rated speed at rated current or less under the load imposed by the device operated.
The rpm affects how fast the thing you are trying to move or do goes. example: motor rpm changes how fast your car goes, but rpm is modified from engine to wheels by gears. Also, in engines, horsepower is directly related to rpm. Basically, rpm times torque = horsepower.
An induction motor is going to cost below a synchronous motor. An induction motor has slip and a synchronous motor does not. check out the 1st paragraph on wiki below. So which a million is greater valuable has greater to do with money than the burden.
As a single parameter RPM of the motor is of no consequence. What is important is the speed of the final moving part or parts of the driven machine. The most commonly used motor is a 4-pole induction motor that runs at a little less than 1800 RPM on 60 Hz power or 1500 RPM on 50 Hz power. A drive train is selected to provide the machine speed that is suitable for the application. In a few cases, the motor can be directly connected without any speed change in the drive train. Some fans and pumps and other machines are designed to work with directly connected motors. In those cases, the available motor speeds must be considered. For AC motors, the available speeds are given by RPM = 120f/p where f is the 50 Hz or 60 Hz power frequency and p is the number of motor poles. The number of poles is an even number, with 2, 4, 6 pole motors being the most common motors with motors becoming progressively less common as the pole number increases. Motors with more poles tend to be available only in higher power ratings. Another level of consideration is whether the motor should run at a constant speed or be equipped with a variable speed control unit. Variable speed is a means of controlling an industrial process to provide: Smoother operation Acceleration control Different operating speed for each process recipe Compensation for changing process variables Slow operation for setup purposes A variable rate of production Accurate positioning Torque or tension control In some cases there are alternative means of controlling the process but variable speed may use less energy or be more convenient.
