find angular speed

Question

One gear wheel turns another, the teeth being on the rims.  The wheels have 10 cm and 30 cm radii, and the smaller wheel rotates at 30rpm.  Find the angular speed of the larger wheel, in radians per second.  

Answer 1

since the outer rims touch, the larger wheel circumference is 2*pi*R = 60*PI

the smaller wheel circumference is 2*pi*10 = 20*PI

 

therefore, smaller wheel will have to turn 3x for every 1 rotation of the larger wheel.

 

So if the ratio of rotations of the smaller wheel to the larger wheel is 3:1, then 30 rpms of the smaller wheel results in 10 rpms of the larger wheel. 

 

Convert rotations per minute to radians per sec:

1 rotation = 2*pi radians

1 min       = 60 sec 

 

10 rotations/min   = 10*(2*pi)/60sec = 20*pi/60 = pi/3  radians/sec for the larger wheel