Answer to Question #101785 in Mechanics | Relativity for kwikiriza steven

Question #101785
angular velocity of a fan increases from
1
20 
rad s
to
1
30 
rad s
in 5s. Find the angular

acceleration and the total angle
1
Expert's answer
2020-01-28T13:36:23-0500

If the fan accelerates from 20 rad/s to 30 rad/s in 5 seconds, its angular acceleration can be found as follows:


α=ΔϕΔt=ω2ω1Δt=30205=2 rad/s2.\alpha=\frac{\Delta\phi}{\Delta t}=\frac{\omega_2-\omega_1}{\Delta t}=\frac{30-20}{5}=2\text{ rad/s}^2.


The total angle:


ϕ=αt22=2522=25 rad.\phi=\frac{\alpha t^2}{2}=\frac{2\cdot 5^2}{2}=25\text{ rad}.


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