Two wheels with fixed centers are in contact with each other and rotate without slipping. Wheel A has a radius of 12.0 cm and is rotating with an angular speed of 35.0 rad/s. Wheel B has a radius of 17.0 cm. What is the angular speed of wheel B?
A) 49.6 rad/s
B) 24.7 rad/s
C) 5.83 rad/s
D) 4.97 rad/s
E) 12.4 rad/s

Question

Quizplus · Accepted Answer

The angular velocity of the two wheels is the same since they are in contact with each other and rotate without slipping. 
ω = ω₁ = ω₂
Therefore, we can use the equation:
v = rω
where v is the tangential velocity and r is the radius. We can assume that the point of contact between the two wheels is not moving (i.e. v = 0) and solve for ω₂:
r₂ω₂ = r₁ω₁
17 cm * ω₂ = 12 cm * 35 rad/s
ω₂ = (12 cm * 35 rad/s) / 17 cm
ω₂ = 24.7 rad/s

Two Wheels with Fixed Centers Are in Contact with Each