A centrifuge in a medical laboratory rotates at an angular speed of 3500 rpm (revolutions per minute). When switched off, it rotates 70.0 times before coming to rest. Find the constant angular acceleration of the centrifuge. (Assume the initial direction of rotation is the positive direction. Indicate the direction with the sign of your answer.)

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To find the constant angular acceleration of the centrifuge, we can use the formula:

ω^2 = ω₀^2 + 2αθ

where ω is the final angular velocity, ω₀ is the initial angular velocity, α is the angular acceleration, and θ is the angle through which the centrifuge rotates.

Given the following information:
ω = 0 (the centrifuge comes to rest)
ω₀ = 3500 rpm = 3500 * 2π/60 rad/s (converting rpm to rad/s)
θ = 70 revolutions = 70 * 2π radians (converting revolutions to radians)

By substituting these values into the formula, we can solve for α:

0^2 = (3500 * 2π/60)^2 + 2α(70 * 2π)

Simplifying the equation:

0 = (3500 * 2π/60)^2 + 2α(70 * 2π)

0 = (3500 * 2π/60)^2 + 140απ

Rearranging the equation:

140απ = -(3500 * 2π/60)^2

Divide both sides by 140π:

α = -(3500 * 2π/60)^2 / (140π)

Now, let's calculate the value:

α = -(3500 * 2π/60)^2 / (140π)
= -(3500 * 2π/60)^2 / 140
≈ -18.47 rad/s^2

Therefore, the constant angular acceleration of the centrifuge is approximately -18.47 rad/s^2. The negative sign indicates that the acceleration is in the opposite direction of the initial (positive) direction of rotation.