In Fig. 10-28, wheel A of radius rA is coupled by belt B to wheel C of radius rC. The angular speed of wheel A is increased from rest at a constant rate α. Find the time needed for wheel C to reach angular speed ω assuming the belt does not slip. (Hint: If the belt does not slip, the linear speeds at the two rims must be equal.) State your answer in terms of the given variables.

Question

FIGURE: imgur . com/QxZR5. gif
(remove spaces and paste)

I tried:
(rA/rC)*α

and

ωC/αC

but said it was wrong.

Answer 1

((Rc)/(ra) * omega)/alpha