Please check my work. We\'re doing a study group and we really don\'t feel confi
ID: 1386174 • Letter: P
Question
Please check my work. We're doing a study group and we really don't feel confident but it seems to make sense.
The fan blade in a jet engine rotates from rest with the angular acceleration alpha=20t3.
(a) Find the angular velocity as a function of time.
(b) find the angular displacement as a function of time.
(c) if the rotational interia of the blade is 15.0 kgm2, find the work done on the blade in the first initial 30 seconds. (Hint: take t from zero to 30 and d-theta=omega-dt)
(a)
(b)
(c)
If someone could please check our work we would greatly appreciate it.
Explanation / Answer
angular accelertation = alfa = rate of change in angular velocity
alfa = dw/dt
dw = alfa*dt
w = integration alfa*dt
part a ) w = 20*t^4/4
part b)
angular displacememnt = w*dt
theta = integration(w*dt)
theta = 20*t^5/20 = t^5
part c)
work = torque*theta
torque = I*alfa
work = I*20*t^3*t^5 = I*20*t^8
dw = 20*I*t^8
w = integrate dW = 20*I*t^9/9
W = (20*15*30^9)/9
W = 6.561e+14 J