Each paddle wheel of a steamer have a mass of 1600 kg and a radius of gyration of 1.2 meters. The steamer turns to port in a circle of 160 meters radius at 24 km/hr. The speed of the paddle is 90 rpm. Determine the magnitude and effect of the gyroscopic couple acting on the steamer.

Consider the wheel shown below with radius R, mass m, and radius of gyration ko¹ The wheel rolls without slipping under the action of a clockwise torque M. At the instant shown the spring with spring constant ks is unstretched. Derive an expression for the velocity of the wheel center of mass G after the center of mass has moved a distance d. (Hint: Use rigid body work-energy principles. The work done to the system by the applied moment is McA0 and A0 can be related to the distace d by the no-slip condition.) Us G R M м, ко ////

6. The turbine of a ship has a mass of 4000 kg. and a radius of gyration of 480 mm. It rotates at 2400 rev/min. clockwise when looking forward from the stern. In each of the following cases determine, the magnitude and indicate clearly with suitable diagrams. the effect of the gyroscopic couple acting on the ship: (a) If the ship, when travelling at 15 ms¹ turns to starboard in a curve 1000 m radius. (b) If the ship is pitching and the bow is descending with maximum velocity. The pitching motion is simple harmonic, the period being 20 seconds and the total angular movement is 12º. (c) If the ship is rolling and at a certain instant has an angular velocity of 0.02 rad. s-¹ clockwise when looking forward from the stern.

The 27-kg wheel has a radius of gyration about its center O of ko = 260 mm, and radius r = 0.5 m. When the wheel is subjected to the constant force F = 354 N, applied to the wheel's center axle at an angle = 6°, it starts rolling from rest. Determine the wheel's angular velocity W (in rad/s) after 3.2 seconds if the wheel has been rolling without slipping. Please pay attention: the numbers may change since they are randomized. Your answer must include 1 place after the decimal point. Take g = 9.81 m/s². F 0 Your Answer: Answer

A drum can rotate about a fixed-point O. The A block is attached to a cord wrapping around the drum. The mass of the drum is md = 100kg and the radius is r = 0.5 m. The radius of gyration of the drum about point O is ko=0.3 m. The mass of the block is mb= 20kg. The block is released from rest. The acceleration due to gravity is g=9.81 m/s2.   (1) Calculate the mass moment of inertia of the drum about the point O, IO_______(kgm2) (two decimal places)

The 4.8-kg rod AB is attached to a collar of negligible mass at A and to a flywheel at B. The flywheel has a mass of 16 kg and a radius of gyration of 180 mm. If the angular velocity of the flywheel is to be the same in the position shown and when point B is directly above C, determine the required value of its angular velocity in the position shown in the figure. 720 mm B 240 mm The required value of angular velocity of the flywheel is rpm (Click to select)

The circular disk of 145-mm radius has a mass of 38 kg with centroidal radius of gyration k bar = 25 mm and has a concentric circular groove of 55-mm radius cut into it. A steady force Tis applied at an angle theta to a cord wrapped around the groove as shown. If T = 40 N, theta = 0, mu_s = 0.11, and mu_k = 0.09, determine the angular acceleration a of the