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 Angle at which a point rotates around a specific axis or center in a given direction. Angular displacement is a vector quantity and has both magnitude and direction. The angle built by an object from its rest point to endpoint created by rotational motion is known as angular displacement. Angular displacement is denoted by θ, and the S.I. unit of angular displacement is radian or rad.

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