A centrifuge accelerates uniformly from rest to 15,000 rpm in 220 s. Through how many revolutions did it turn in this time?
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To calculate the number of revolutions, we first need to convert the final angular velocity from rpm to revolutions per second (rev/s). Then, we can use the formula for angular displacement to find the total number of revolutions.
Given: Initial angular velocity (ωi) = 0 rpm Final angular velocity (ωf) = 15,000 rpm Time (t) = 220 s
Convert final angular velocity to rev/s: ωf = (15,000 rpm) * (1 min / 60 s) * (1 rev / 1 rpm) = 250 rev/s
Use the formula for angular displacement: θ = ωi * t + (1/2) * α * t^2
Since the centrifuge starts from rest, ωi = 0.
θ = (1/2) * α * t^2 α = (ωf - ωi) / t α = (250 rev/s - 0 rev/s) / 220 s = 1.136 rev/s^2
θ = (1/2) * (1.136 rev/s^2) * (220 s)^2 θ ≈ 13,726 rev
Therefore, the centrifuge turned approximately 13,726 revolutions in 220 seconds.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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