164 KINETICS OF A RIGID BODY. [304. 



(3) A circular disc of radius r revolves uniformly about its axis, 

 making 100 revolutions per minute. What is its kinetic energy? 



(4) A fly-wheel of radius r, in which a mass, equal to that of the disc 

 in Ex. (3), is distributed uniformly along the rim, has the same angular 

 velocity as the disc. Neglecting the mass of the nave and spokes, 

 determine its kinetic energy, and compare it with that of the disc. 



(5) A fly-wheel of 12 ft. diameter, whose rim weighs 12 tons, makes 

 50 revolutions per minute. Find its kinetic energy in foot-pounds. 



(6) A fly-wheel of radius r and mass m is making ^V revolutions per 

 minute when the steam is shut off. If the radius of the shaft be r\ and 

 the coefficient of friction /u,, find after how many revolutions the wheel 

 will come to rest owing to the axle friction. 



(7) A fly-wheel of 10 ft. diameter, weighing 5 tons, is making 40 

 revolutions when thrown out of gear. In what time does it come to 

 rest if the diameter of the axle is 6 in. and the coefficient of friction 

 fj. = 0.05 ? 



(8) A uniform straight rod of length /is hinged at one end so as to 

 turn freely in a vertical plane. If it be dropped from a horizontal 

 position, with what angular velocity does it pass through the vertical 

 position? (Equate the kinetic energy to the work of gravity.) 



304. Impulses. Suppose a rigid body with a fixed axis is 

 acted upon, when at rest, by a single impulse F, in a plane 

 perpendicular to the axis and at the distance / from the axis. 

 It is required to determine the initial motion of the body just 

 after impact. 



As the impulsive reactions of the fixed axis have no moment 

 about this axis, the initial angular momentum of the body about 

 the fixed axis must be equal to the moment of the impulse F 

 about the same axis ; i.e. to Fp. If co is the initial angular 

 velocity, the momentum of a particle m at the distance r from 

 the axis is mwr\ hence the angular momentum of the body 

 = 2ma>r*=co2mr 2 =ci)f, where / is the moment of inertia of the 

 body for the fixed axis. Hence we have 



<*=- (ii) 



