136.] ROTATION. 69 



136. Exercises. 



(1) If a fly-wheel of 12 ft. diameter makes 30 revolutions per 

 minute, what is its angular velocity, and what is the linear velocity of a 

 point on its rim? 



(2) A pulley 5 ft. in diameter is driven by a belt travelling 500 ft. 

 a minute. Neglecting the slipping of the belt, find (a) the angular 

 velocity of the pulley in radians, and (^) its number of revolutions per 

 minute. 



(3) Find the constant acceleration (such as the retardation caused by 

 a Prony brake) that would bring the fly-wheel in Ex. (i) to rest in 1 

 minute. 



(4) How many revolutions does the fly-wheel in Ex. (3) make 

 during its retarded motion before it comes to rest? 



(5) A wheel is running at a uniform speed of 32 turns a second 

 when a resistance begins to retard its motion uniformly at the rate of 8 

 radians per second, (a) How many turns will it make before stopping? 

 (l>) In what time is it brought to rest ? 



(6) A belt runs over two pulleys turning about parallel axes. Show 

 that the angular velocities of the pulleys are inversely proportional to 

 their diameters. Do the pulleys rotate in the same or opposite sense ? 



