A wheel starts from rest and rotates with a constant angular acceleration about a fixed axis. It completes the first revolution 6.0 s after it started. How long after it started will the wheel complete the second revolution?
A) 9.9 s
B) 7.8 s
C) 8.5 s
D) 9.2 s
E) 6.4 s

Question

Quizplus · Accepted Answer

Let the angular acceleration be represented by α in rad/s^2 and let the time taken to complete the second revolution be t.

During the first revolution, the angular displacement of the wheel is 2π radians and the time taken is 6 seconds.

Using the formula:
θ = ωi * t + 1/2 * α * t^2
where θ = 2π, ωi = 0 (as the wheel starts from rest), and t = 6 seconds

2π = 0 + 1/2 * α * (6)^2
2π = 18α
α = π/9 rad/s^2

Now, using the same formula for the second revolution, we have:
θ = ωi * t + 1/2 * α * t^2
where θ = 4π (as it completes two revolutions), ωi = 0 (as it starts from rest), and α = π/9 rad/s^2

4π = 0 + 1/2 * (π/9) * t^2
t^2 = 72
t = 8.5 seconds

Therefore, the wheel will complete the second revolution 8.5 seconds after it started. Thus, the best choice is C.

A Wheel Starts from Rest and Rotates with a Constant