A centrifuge is a common laboratory instrument that separates components of differing densities in solution. This is accomplished by spinning a sample around in a circle with a large angular speed. Suppose that after a centrifuge in a medical laboratory is turned off, it continues to rotate with a constant angular deceleration for 11.6 s before coming to rest.

(a) If its initial angular speed was 4110 rpm, what is the magnitude of its angular deceleration?

Convert 4110 rpm to radians per second, and divide the result by 11.6 s.

The dimensions of the angular acceleration will be radians/sec^2

thank you, I initially thought of doing that but it was the wrong answer. Thank you though!

Did you get 430 rad/s for the initial angular velocity?

That actually sounds low for a modern centrifuge.

To find the magnitude of the angular deceleration, we need to use the following equation:

ω^2 = ω₀^2 + 2αθ

Where:
ω: Final angular velocity (0 rad/s in this case because it comes to rest)
ω₀: Initial angular velocity (4110 rpm converted to rad/s)
α: Angular acceleration or deceleration
θ: Angle through which the centrifuge rotates (unknown, but we don't need it for this question)

Rearranging the equation, we get:

α = (ω^2 - ω₀^2) / (2θ)

Given:
ω = 0 rad/s
ω₀ = 4110 rpm = 4110 * (2π/60) rad/s

Plugging in these values into the equation, we get:

α = (0 - (4110 * (2π/60))^2) / (2θ)

We can calculate α if we can find the value of θ. However, the problem only gives us the time (11.6 s) during which the centrifuge decelerates, not the angle θ.

To find θ, we need another equation that relates the angular displacement (θ) to the angular acceleration or deceleration (α) and time (t):

θ = ω₀t + (1/2)αt^2

Plugging in the given values, we get:

θ = (4110 * (2π/60) * 11.6) + (1/2) * α * (11.6^2)

Since we want to find the magnitude of the angular deceleration (α), we can solve this equation for α:

α = (2θ - 4110 * (2π/60) * 11.6) / (11.6^2)

Unfortunately, we cannot solve for α because we still do not have the value of θ. Therefore, we cannot determine the magnitude of the angular deceleration with the given information.