Final answer:
The total angular displacement of the centrifuge can be calculated using the equation: Δθ = ½ωinitialt2 + αt2. In this example, the initial angular velocity is zero, the time taken is 30 seconds, and the angular acceleration can be calculated using the formula α = (ωfinal - ωinitial)/t. Substituting the values into the equation, the total angular displacement is Δθ radians.
Step-by-step explanation:
The total angular displacement of the centrifuge can be calculated using the equation:
Δθ = ½ωinitialt2 + αt2
Where Δθ is the total angular displacement, ωinitial is the initial angular velocity, t is the time taken, and α is the angular acceleration.
In this example, the initial angular velocity is zero as the centrifuge starts from rest and the time taken is 30 seconds. The angular acceleration can be calculated using the formula α = (ωfinal - ωinitial)/t.
Substituting the values into the equation, we get:
Δθ = ½(0)(302) + (ωfinal - 0)(302)
Therefore, the total angular displacement of the centrifuge is Δθ radians.