(II) A merry-go-round accelerates from rest to 0.68 rad/sin 34 s. Assuming the merry-go-round is a uniform disk ofradius 7.0 m and mass 31,000 kg, calculate the net torquerequired to accelerate it.

An amusement park ride (known variously as the Rotor, the Turkish Twist and the Graviton) consists of a large vertical cylinder that is spun about it axis fast enough such that the riders remain pinned against its inner wall. The floor drops away once the cylinder has attained its full rotational speed. The radius of the cylinder is R and the coefficient of static friction between a rider and the wall is us. (i)Show that the minimum FAICT angular speed necessary to keep a rider from falling is given by o = √g/us R. (ii) Obtain a numerical value for frequency in revolutions per minute if R = 4 m and us = 0.4. encloso TOO 07 Fig. Ex. 44; The rotor (an amusement park ride) (For reference only)

(II) A ball of mass M and radius r on the end of a thin massless rod is rotated in a horizontal circle of radius Ro about an axis of rotation AB, as shown in Fig. 10-58. (a) Considering the mass of the ball to be concentrated at its center of mass, calculate its moment of inertia about AB. (b) Using the parallel-axis theorem and considering the finite radius of the ball, calculate the moment of inertia of the ball about AB. (c) Calculate the percentage error intro- duced by the point mass approximation for r 1.0 m. s 9.0 cm and %3D Ro to Toinso odt 1s oizs IsB gadsion ai m %3D 08.2 (E 10-0 boT Ro UKE or da Problem 89. ► M 10-65 FIGURE 10-58 molecule. The H bonds incrtia Problem 58. A gl00A

16-146. A ride in an amusement park consists of a rotating arm AB that has an angular acceleration of aдB = 1 rad/s² QAB when @AB = 2 rad/s at the instant shown. Also at this instant the car mounted at the end of the arm has an angular acceleration of a = {-0.6k) rad/s² and angular velocity of w' (-0.5k) rad/s, measured relative to the arm. Determine the velocity and acceleration of the passenger C at this instant. = w' = 0.5 rad/s 10 ft 60° y WAB = 2 rad/s 30° x Probs. 16-145/146 B 2 ft