Imagine a monkey is sitting inside a barrel turned on its side. A cruel elephant pushes the barrel down a hill and the monkey starts to roll inside the barrel. This particular monkey gets motion sickness, and an outside observer has noticed that if the monkey spins more than once per second, the monkey will likely vomit. The barrel rolls perfectly down the slope (without slipping) and the outside observer calculates the angular acceleration of the barrel to be 1.2rad/s2. The barrel has a diameter of 1.5 m. (a) How long will it take for the monkey to spin fast enough to vomit?
(b) How far will the monkey have rolled before vomiting?
(c) How many times will the monkey have made a complete circle before vom- iting?
(d) 50kg. Further, the hill was the perfect size to make this monkey vomit - at the bottom of the hill, the monkey is rotating fast enough that it vomits. Furthermore, the observer measured that the hill is 8.4 m tall. Using all of this data, what is the moment of inertia of the monkey-and-barrel system, rotating about the central axis of the barrel?