one gear wheel turns another

Question

One gear wheel turns another the teeth being on the rims. The wheels have 40cm and 50cm radii, and the smaller wheel rotates at 20rpm. find angular speed of larger wheel in radians per second

Answer 1

First, convert the rotation rate of the smaller gear, 20 revolutions per minute, into radians per second:

 

     (20 rev/min)*(2pi rad/rev.)*(1 min/60 sec) = 2pi/3 rad/sec

 

The larger gear will rotate at 40/50 = 4/5 the rate pf the smaller gear:

 

     (2pi/3 rad/sec) *(4/5) = (8pi/15) rad/sec