A centrifuge in a biology laboratory rotates at an angular speed of 3,400 rev/min. When switched off, it rotates 48.0 times before coming to rest. Find the constant angular acceleration of the centrifuge (in rad/s2). Consider the direction of the initial angular velocity to be the positive direction, and include the appropriate sign in your result.

Question

Jonah Bryant

Physics

20 August, 19:54

A centrifuge in a biology laboratory rotates at an angular speed of 3,400 rev/min. When switched off, it rotates 48.0 times before coming to rest. Find the constant angular acceleration of the centrifuge (in rad/s2). Consider the direction of the initial angular velocity to be the positive direction, and include the appropriate sign in your result.

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Phillip Holloway · Answer 1

- 210 rad/s²

Explanation:

n = frequency of rotation = 3400/60 = 170/3 per sec.

angular velocity ω (0) at time 0 = 2π n = 2π x 170/3

angular velocity at time t = ω (t) = 0

now, ω² (t) = w² (o) + 2α Φ (α = angular acceleration and Φ = angular displacement) = 2π x 48 rad.

0 = (2π x 170/3) ² + 2α x 48 x 2π

α = - (2π x 170 x 170) / (3 x 3 x 2 x 48) = 210 rad / s²