A long string is wrapped around a 6.3-cm-diameter cylinder, initially at rest, that is free to rotate on an axle. The string is then pulled with a constant acceleration of 2.0 m/s2 until 1.3 m of string has been unwound. If the string unwinds without slipping, what is the cylinder's angular speed, in rpm, at this time?

You have a 1.00 m long string with a bob attached to its end. You are swinging it around your head, and it completes 1.00 whole revolution every 2.00 s. What is its tangential speed, in m/s? Answer with 3 significant figures.

The ability of the human eye to rapidly rotate was studied using contact lenses fitted with accelerometers. While a subject, whose eyeball has radius 1.25 cm, watches a moving object her eyeball rotates through 20.0° in a time interval of 69.6 ms. a. What is the magnitude of the average angular velocity of the eye?  asnwer in rad/s 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? answer in rad/s^2 c. What tangential acceleration would the contact-lens accelerometers record in this case? answer in m/s^2

The cable lifting an elevator is wrapped around a 1.0-m-diameter cylinder that is turned by the elevator’s motor. The elevator is moving upward at a speed of 1.6 m/s. It then slows to a stop as the cylinder makes one complete turn at constant angular acceleration. How long does it take for the elevator to stop?