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A centrifuge in a medical laboratory rotates at an angular speed of 3,750 rev/min. When switched off, it rotates through 48.0 revolutions before coming to rest. Find the constant angular acceleration (in rad/s²) of the centrifuge.


______rad/s²

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The constant angular acceleration (in rad/s²) of the centrifuge is 255.66 rad/s².

Constant angular acceleration of the centrifuge

The constant angular acceleration of the centrifuge is calculated as follows;

ωf² = ωi² - 2αθ

where;

  • ωf is the final angular velocity
  • ωi is initial angular velocity
  • θ is angular displacement
  • α is angular acceleration

When the centrifuge is switched off, the final angular velocity = 0

Initial angular velocity: ωi = 3,750 rev/min x 2π rad/rev x 1 min/60 s = 392.7 rad/s

angular displacement: θ = 48 rev = 48 rev x 2π rad/rev = 301.6 rad

0 = ωi² - 2αθ

2αθ = ωi²

α = ωi²/2θ

α = (392.7²) / (2 x 301.6)

α = 255.66 rad/s²

Thus, the constant angular acceleration (in rad/s²) of the centrifuge is 255.66 rad/s².

Learn more about angular acceleration here: https://brainly.com/question/25129606

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