Electronic – How to work out what resistor to use

In your example, you've paid too much money and the part is huge (especially the 100W part). If the LED current is an AC signal (PWM or whatever) the 100W resistor may have a lot of inductance, which will change the way the circuit behaves.

On the other hand, the ratings of resistors are conditional on a bunch of things, such as mounting, surrounding PCB patterns (especially SMT resistors) and, of course, ambient temperature. The number in the part description is just sort of a rough guide, you really have to drill down using datasheets and part series manuals and other manufacturer's data to get the details. You should also consider odd conditions such as extremes of input voltage, what happens if an LED shorts out, and so on.

It is also not a good idea to get too close to the maximum ratings if you want long life. Using a 1/4W part for 1/8W actual dissipation is not a bad idea. Using a 1W part might make sense if it's a high-reliability design or you have a bunch of them on hand. Using a 100W part is silly.

The usual procedure I use for motors is through a H-Bridge. But since a vibration motor isn't bidirectional I believe we can use just one switch in the following configuration. (I'm assuming its a 3V motor).

Instead of the D3 pin used on the arduino you can use the GPIO pin from the RPi. Furthermore you can also use the 5V output from the Raspberry pi for testing, otherwise i usually like to use an external battery for this.

Source for further reading:

http://learningaboutelectronics.com/Articles/Vibration-motor-circuit.php