Angular Speed Between 2 rims attached by a belt

[dimmermanj]

So I'm new to the Physics Forums and am looking for some help on this problem:

Wheel A of radius r=10cm is coupled by belt B to wheel C with radius R=25cm.
the angular speed of wheel A is increased from rest at a constant rate of 1.6 rad/s^2.
Find the time needed for wheel C to reach an angular speed of 100 rev/min, assuming the belt does not slip (hint: the linear speeds of the two rims must be equal)

I get really confused whenever dealing with angular speed so if anyone could help that'd be great!

thanks
Jim

 

[LightHero]

Solution:First, convert the angular speed of wheel C to rad/s by multiplying it by 2π, giving a goal angular speed of 637.83 rad/s.Since the rims must have equal linear speeds, we can use the formula for linear speed (v=rw). So the linear speed of both rims must be w(10 cm)=637.83 rad/s. We can then use the equation for acceleration (a=2Δw/Δt) to calculate the time needed to reach the desired angular speed:Δt=(2*637.83)/(1.6) = 1600 s Therefore, the time needed for wheel C to reach an angular speed of 100 rev/min is 1600 seconds.