Answer :
The constant angular acceleration of the wheel is approximately 27.207 rad/s². Using the kinematic equation that relates angular displacement and angular acceleration.
We can use the kinematic equation that relates angular displacement, initial angular velocity, final angular velocity, and angular acceleration:
θ = θ₀ + ω₀t + 0.5αt²
Where:
θ = angular displacement (in radians)
θ₀ = initial angular displacement (0, since it starts from rest)
ω₀ = initial angular velocity (0, since it starts from rest)
α = angular acceleration (what we want to find)
t = time interval (2.93 seconds)
Given that the wheel rotates through 37.0 revolutions, which is equivalent to 2π * 37.0 radians, and the final angular velocity is 98.5 rad/s, we can rewrite the equation as:
2π * 37.0 = 0 + 0 + 0.5α(2.93)²
Solving for α:
2π * 37.0 = 0.5α * 8.5649
Now, solve for α:
α = (2π * 37.0) / 8.5649
α ≈ 27.207 rad/s²
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