A wheel of radius 0.5 m rolls without sliding on a horizontal surface as shown. Starting from rest, the wheel moves with constant angular acceleration 6 rad/s². The distance in traveled by the center of the wheel from t = 0 to t = 3 s is: A) zero B) 27 m C) 13.5 m D) 18 m E) none of these

Question

Quizplus · Accepted Answer

Let's first find the angular velocity at t=3s using the formula: 
ω = ω0 + αt 
where ω0 = 0 (starting from rest), α = 6 rad/s^2, and t = 3s 
ω = 0 + 6(3) = 18 rad/s

Now, let's find the distance traveled by the center of the wheel using the formula: 
s = rθ 
where r = 0.5m (radius of the wheel) and θ is the angle rotated by the wheel in radians

To find θ, we can use the formula: 
θ = ω0t + 0.5αt^2 
where ω0 = 0 (starting from rest), α = 6 rad/s^2, and t = 3s 
θ = 0 + 0.5(6)(3)^2 = 27 rad

Therefore, the distance traveled by the center of the wheel is: 
s = rθ = (0.5)(27) = 13.5 m

So, the best choice is C.

A Wheel of Radius 0