Question

A wheel of radius 10cm is coupled with belt to another wheel of radius 30cm 1st wheel moves with angular acceleration 1.57rad/s . After how much 2nd wheel will get angular velocity 100m/s

Answer 1

let RA and RC be the angular speed of wheel A and C respectively 
then linear speed of belt B = RA*rA = RC*rC 
hence RA= RC * rC/rA = RC 25/10 = 2.5 RC 

When C reach 100 rev/min 
then A reach 2.5 100 = 250 rev/min 
RA = RAo + a*t = 0 + 1.6 t rad / sec 
RA = 1.6 t /(2*pi) = 1.6 t /6.28 =0.2548 t rev/sec =15.288 t rev/min 
15.288 t = 250 
t = 250/15.288 = 16.35 seconds