B 24 in. A e 12 in. з

Problem 4. A thin, semi-circular ring of mass m and radius R is pinned to ground at point O. The bar is released from rest in the position shown. Note that a = 2R, IG = mR² - ma² (a) Find the mass moment of inertia of the body about point O (b) Find the angular acceleration of the ring when released (c) Find the reaction forces on the ring at point O Ans: (b) a=0.5(g/R); (c) Ox = (mga)/(2R), Oy = mg/2 6.0 g G a -R-

Pravinbhai

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.

An automobile wheel test rig consists of a uniform disk A, of mass mà = 5000 kg and radius rà = 1.5 m, that can rotate freely about its fixed center C and over which the wheel of an automobile is made to roll. A wheel B, whose center and center of mass coincide at D, is mounted on a shaft (not shown) that holds D fixed while it allows the wheel to rotate about D. The wheel has diameter d = 0.62 m, mass mß = 21.5 kg, and mass moment of inertia about its mass center /D = 44 kg-m². Both A and B are initially at rest when B is subject to a constant torque M that causes B to roll without slip on A. M B d A If M = 1200 N·m, use the angular impulse-momentum principle to determine how long it takes to reach conditions simulating a car speed of 100 km/h. The automobile wheel test rig takes s to reach conditions simulating a car speed of 100 km/h.

Parvinbhai

Please answer this in 20 mins