A wheel of radius 0.4 meters starts from rest and experiences a constant angular acceleration of 5 rad/s². Calculate the time it takes for the wheel to complete one full revolution.
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To calculate the time it takes for the wheel to complete one full revolution, we need to find the time it takes for the wheel to reach an angular displacement of 2π radians.
We can use the kinematic equation:
θ = ω₀t + (1/2)αt²
where
θ = final angular displacement = 2π rad
ω₀ = initial angular velocity = 0 rad/s
α = angular acceleration = 5 rad/s²
t = time
Rearranging the equation, we get:
2π = (1/2)(5)t²
Simplifying, we have:
4π = 5t²
Dividing both sides of the equation by 5, we get:
t² = (4π/5)
t ≈ √(4π/5)
t ≈ 1.26 seconds
Therefore, it takes approximately 1.26 seconds for the wheel to complete one full revolution.
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