Here is an interesting short video that shows how intensely cymbals vibrate when you hit them. It's important to be aware of this for two main reasons.
1. You always want to hit the cymbal with proper technique, allowing the stick to come off the cymbal after you hit it. This ensures that all of the reactionary force the cymbal exerts will be expelled freely into the air, allowing the cymbal to produce sound and not send all of those vibrations back into your hand and arm.
2. Always use cymbal sleeves. A cymbal sleeve is a small plastic piece that eliminates metal on metal contact between a cymbal and stand. If you don't use cymbal sleeves, that metal on metal contact can crack your cymbals.