How a Stroboscope Works
A stroboscope is a light that can turn on and off very rapidly. One flash is separated from the next by a specific, repeated time interval. The time interval is variable --- you can make it longer or shorter --- and it's usually stated in terms of repetition rate. For example, a rep rate of 3,000 flashes per minute corresponds to a time interval of 1/50th of a second between flashes. To see the principle in action, place the stroboscope so it illuminates the surface of a table, and roll a ball across it. Darken the other lights in the room, and the smooth motion of the ball will appear to be broken into tiny steps, as the ball is only visible at intervals of 1/50th of a second.
Acceleration
You can roll the ball off the edge of the table. As the ball falls, it's accelerated by the force of gravity. Because of this acceleration, in each 50th of a second, it will move a little further than it did in the previous 50th of a second. Adjust the repetition rate of the strobe light so enough images appear to make the change in velocity apparent, but not so many as to make it difficult to distinguish the image in separate flashes. For example, you could go down to 10 Hertz, which is 10 flashes per second, and illustrate the acceleration of gravity. You can observe in real-time, or take video or a long-exposure still photograph to do quantitative measurements.
Vibration
A hammered piano string creates sound by vibrating. The form of that vibration is usually invisible. If you closely observe a vibrating string, you can see it's "fuzzy," with its edges blurred by motion, but it's difficult to see what that motion looks like. A strobe light will make that motion clear. It's easier to set up an experiment with a tightly strung string than with a piano, but the principle is the same. Pluck the string and adjust the rep rate of the stroboscope to "freeze" the motion. When properly adjusted, the strobe light will capture the string every time it's in the same position as it repeats its vibration, making the form of the wave visible.
Rotation
One of the first applications of strobe lights was to motors. A motor repeats its movements, but so quickly that the human eye can't see them. When the strobe is matched to the rotation rate of the motor, the position of the motor's parts at that part of its cycle will become clear. You can see how this works by painting one blade of a fan, then adjusting the strobe light so it flashes when the colored blade is only in one position. That could happen if the fan rotates once between exposures, but also if it rotates twice between flashes, or 12 times between flashes, or any other whole number of times. If you want to measure the rate of rotation, you have to lower the interval between flashes to make sure you're at the highest repetition rate that freezes the motion.