A study was done observing the ability of the eye to rapidly rotate in order to follow a moving object by placing contact lenses that contain accelerometers on a subject’s eye. The eyeball has radius 1.25 cm. Suppose that, while the subject watches a moving object, the eyeball rotates through 20.0° in a time interval of 75 ms. 

(a) What is the magnitude of the average angular velocity of the eye? 

(b) 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? 

(c) What tangential acceleration would the contact-lens accelerometers record in this case?