At its lowest setting a centrifuge rotates with an angular speed of ω1 = 250 rad/s. When it is switched to the next higher setting it takes t = 8.5 s to uniformly accelerate to its final angular speed ω2 = 750 rad/s. 1) Calculate the angular acceleration of the centrifuge α1 in rad/s2 over the time interval t. α1 = 2) Calculate the total angular displacement (in radians) of the centrifuge, Δθ, as it accelerates from the initial to the final speed. Δθ =

At its lowest setting a centrifuge rotates with an angular speed of ω1 = 250 rad/s. When it is switched to the next higher setting it takes t = 8.5 s to uniformly accelerate to its final angular speed ω2 = 750 rad/s. 1) Calculate the angular acceleration of the centrifuge α1 in rad/s2 over the time interval t. α1 = 2) Calculate the total angular displacement (in radians) of the centrifuge, Δθ, as it accelerates from the initial to the final speed. Δθ =

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Question

At its lowest setting a centrifuge rotates with an angular speed of ω₁ = 250 rad/s. When it is switched to the next higher setting it takes t = 8.5 s to uniformly accelerate to its final angular speed ω₂ = 750 rad/s.

1) Calculate the angular acceleration of the centrifuge α₁ in rad/s² over the time interval t. α₁ =

2) Calculate the total angular displacement (in radians) of the centrifuge, Δθ, as it accelerates from the initial to the final speed. Δθ =

Definition Definition Rate of change of angular velocity. Angular acceleration indicates how fast the angular velocity changes over time. It is a vector quantity and has both magnitude and direction. Magnitude is represented by the length of the vector and direction is represented by the right-hand thumb rule. An angular acceleration vector will be always perpendicular to the plane of rotation. Angular acceleration is generally denoted by the Greek letter α and its SI unit is rad/s 2 .

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