Chapter 21, Problem 78P

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)

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 g=9.81 m/s2 .   (2) ) If the mass moment of inertia of the drum about point O is IO, and the angular acceleration of the drum is α, select the correct moment equation of the whole drum-block system about the point O._____________       A. mbgr=rmb(rα)   B. 0   C. mbgr=Ioα +rmb(rα)   D. mbgr=Ioα

An aeroplane makes a complete half circle of 70 metres radius, towards left, when flying at 500 km per hr. The rotary engine and the propeller of the plane has a mass of 600 kg and a radius of gyration of 0.3 m. The engine rotates at 2500 r.p.m. clockwise when viewed from the rear. Find the gyroscopic couple on the aircraft.

1) The shown spool has a mass of 100 kg and radius of gyration of 0.3 m. For P = 70 N and µ, =H = 0.2 the spool rolls without sliding, calculate the angular acceleration of the spool 250 mm 400 mm

The center of the 173-lb wheel with centroidal radius of gyration of 5.6 in. has a velocity of 3.4 ft/sec down the incline in the position shown. Calculate the normal reaction N under the wheel as it rolls past position A. Assume that no slipping occurs. 36° 24" 17" Aj Answer: N = i Ib

The 60-kg unbalanced wheel rolls without slipping on the horizontalplane. The radius of gyration of the wheel about its mass center G is 240 mm.Calculate the kinetic energy of the wheel in the position shown, where its angular velocity is ω=2 rad/s.

An aeroplane runs at 600 km/ h. The rotor of the engine weighs 4000 N with radius of gyration of 1 metre. The speed of rotor is 3000 rpm in anticlockwise direction when seen from rear side of the aeroplane. If the plane takes left turn in a curve of 100 metres radius, find: 1. gyroscopic couple developed; and 2. effect of reaction gyroscopic couple developed on the body of aeroplane by using vector diagram.

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.

The rigid body (slab) has a mass m and rotates with an angular velocity es about an axis passing through the fixed point 0. Show that the momenta of all the particles composing the body can be represented by a single vector having a magnitude mvg and acting through point P, called the center of percussion, which lies at a distance TPIG - ka/rajo from the mass center G. Here kg is the radius of gyration of the body, computed about an axis perpendicular to the plane of motion and passing through G.