Her: I hate dancing with glasses.
Me: Because they fall off when you’re doing the turn-y things?
Her: Yes, it’s so much easier with contacts.
Me: You know, you can calculate how fast you’d have to turn to get the contacts to pop out.
How fast would a dancer have to spin to get her contacts to pop out?
Contact lenses weigh about 0.05 g and are about 1.0 cm2 in area. They are held on mostly by suction. Suction occurs because there is a partial vacuum created under the contact as it's pulled away from the eye. To pop out, a contact needs to overcome air pressure, which for our atmosphere is about 100 kPa. As the dancer spins, her contacts move in a circle with roughly a 10 cm radius. The force to keep an object in uniform circular motion is given by
force = (mass) · (velocity)2/ (radius).
The maximum this force can be before the contact pops out is determine by atmospheric pressure
force = (pressure) · (area).
Solving for the velocity, we get
velocity = [(pressure) · (area) · (radius) / (mass)]1/2
= [(100 kPa) · (1 cm2) · (10 cm) / (0.05 g)]1/2
= 140 m/s.
A dancer would have to rotate about 1400 per second to get her contacts to pop out.