A fan blade rotates with angular velocity given by z ( t )= t 2, where = 5.50 ra

Question

A fan blade rotates with angular velocity given by z(t)= t2, where = 5.50 rad/s and = 0.820 rad/s3

Part A.) Calculate the angular acceleration as a function of time. (answer az(t)=?)

I got -1.64 but it said that the correct answer involves the variable , which was not part of your answer.

Part B.) Calculate the instantaneous angular acceleration z at t0 = 3.1 s . (answer az=? rad/s^2)

Part C.) Calculate the average angular acceleration avz for the time interval t=0 to t0 = 3.1 s . (answer aaz-z=? rad/s^2)

Explanation / Answer

A) we know, angular acceleration, alfa_z = dw/dt

= -beta*2*t

= -2*beta*t

B) at t = 3.1 s

alfa_z = -2*0.82*3.1

= -5.084 rad/s^2

C) at t = 0,

w1 = gamma - beta*t^2

= 5.5 - 0.82*0^2

= 5.5 rad/s

at t = 3.1 s

w2 = 5.5 - 0.82*3.1^2

= -2.38 rad/s

average angular acceleration , alfa_avg = (w2 - w1)/(t2 - t1)

= (-2.38 - 5.5)/(3.1 - 0)

= -2.54 rad/s^2

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