Answer :
the magnitude of the centrifuge's angular acceleration is approximately 13.07 rad/s². To find the angular acceleration of the centrifuge, we'll first determine its angular velocity, then use the angular kinematic equation to calculate the angular acceleration. We'll use these terms in our explanation: angular acceleration (α), angular velocity (ω), initial angular velocity (ω₀), time (t), linear velocity (v), and radius (r).
1. Find the angular velocity (ω):
Given that the linear velocity of a point 7.3 cm (0.073 m) from the axis is 124 m/s, we can use the formula:
v = rω
Solving for ω:
ω = v / r = 124 m/s / 0.073 m ≈ 1698.63 rad/s
2. Use the angular kinematic equation to find the angular acceleration (α):
Since the centrifuge starts from rest, the initial angular velocity (ω₀) is 0. The equation is:
ω = ω₀ + αt
Solving for α:
α = (ω - ω₀) / t = (1698.63 rad/s - 0 rad/s) / 130 s ≈ 13.07 rad/s²
Therefore, the magnitude of the centrifuge's angular acceleration is approximately 13.07 rad/s².
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