Answer to Question #88563 in Mechanics | Relativity for Evelyn

Question

If a coin initially lands heads up and then it’s flipped and goes straight up from a table with initial velocity v=3m/s. It rotates in the air with angular velocity ω=20 rad/s and falls back down to the table. Does the coin land heads or tails? Ignore air resistance. I’m having a hard time answering this question and I can’t seem to find a formula to use!

Answer 1

All we need to do is to determine by what angle the coin will rotate during its flight in the air. First, we determine the time of flight t. The coin starts with velocity v = 3 m/s directed upwards, and falls back on the table with the same velocity directed downwards. Hence, the absolute change in velocity during the flight is 2v. This change is due to the acceleration of gravity g = 9.8 m/s², whence we have an equation 2v = gt. Hence, the time of flight is t = 2v/g = (6/9.8) s = 0.6 s. During this time, the coin will perform ωt / 2π = 20×0.6 / 2π = 1.9 rotations, which is only 0.1 of a rotation less than two complete rotations. Since 0.1 is less than a quarter, the coin will land on the same face as it would after two complete rotations, i.e., it will land on the same face on which it landed the first time. Thus, the coin will land heads up.

Answer: It will land heads up.