Problem: A fan blade rotates with angular velocity given by ωz(t)= γ − β t2, where γ = 4.85 rad/s and β = 0.780 rad/s3.a- Calculate the angular acceleration as a function of time t in terms of β and γ. Express your answer in terms of some or all of the variables β, γ, and t.b- Calculate the instantaneous angular acceleration αz at t0 = 3.3 s. c- Calculate the average angular acceleration αav−z for the time interval t=0 to t0 = 3.3 s.

FREE Expert Solution

a-

Angular acceleration:

a=dωz(t)dt

a=ddt(γ-βt2)

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Problem Details

A fan blade rotates with angular velocity given by ωz(t)= γβ t2, where γ = 4.85 rad/s and β = 0.780 rad/s3.

a- Calculate the angular acceleration as a function of time t in terms of β and γ. Express your answer in terms of some or all of the variables β, γ, and t.

b- Calculate the instantaneous angular acceleration αz at t0 = 3.3 s. 

c- Calculate the average angular acceleration αav−z for the time interval t=0 to t0 = 3.3 s.