How to solve this pulley problem?

Question

A pulley with a diameter of 14 inches is running at 140 rpm while belted to a 28 inch pulley. Find the speed of the larger pulley.

Answer 1

Small pulley diameter,d1=14 in.

Radius of the the small pulley,r1=d1/2

                                              =14/2=7 in.

Speed of the small pulley,omega1=140 rpm

Large pulley diameter,d2=28 in.

Large of the the small pulley,r2=d2/2

                                             =28/2=14 in.

Use the relation

r1*omega1=r2*omega2

omega2=r1*omega1/r2

               =7*140/14

               =70 rpm

Speed of the large pulley,omega2=70 rpm