Question

Required information The ability of the human eye to rapidly rotate was studied using contact lenses fitted with accelerometers. While a subject, whose eyeball has radius 125 cm, Watches a moving object her eyeball rotates through 20.0' in a time interval of 68.6 ms. Assume that the eye starts at rest, rotates with a constant angular acceleration during the first half of the interval, and then the rotation slows with a constant angular acceleration during the second half until it comes to rest. What is the magnitude of the angular acceleration of the eye? rad/s2

what is the magnitude of the angular acceleration if the eye?

Answer 1

Δθ = 20 /2 = 10 deg = 10 *pi /180 = pi /18 rad  

ωi = 0 and   Δt = 68.6/2 = 34.3 ms =34.3 *10^-3 sec

Δθ = ωi *Δt + 1/2*α* Δt^2

pi /18 = 0 + 0.5*α * (34.3 *10^-3)^2

from here  α ≈ 296.701 rad/s²

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