I have a small quadcopter equipped with the MPU6050, which has a built-in accelerometer and gyroscope. It is able to sample the acceleration at 1 kHz and the angular velocities at 8 kHz. However, I only sample them at 200 Hz. I placed my drone indoors before a large fan to see how it responds, and the typical readings look like this:
These are raw signals. They have only been converted to the proper units. Why is the angular velocity so much smoother than the acceleration? The only guess I have is that the MPU6050 is averaging the measurements each time I sample: so for acceleration it can average 5 measurements (1000/200), while for the angular velocity it can average 40 measurements (8000/200).