At t = 0 the current to a dc electric motor is reversed, resulting in an angular

Question

At t = 0 the current to a dc electric motor is reversed, resulting in an angular displacement of the motor shaft given by theta(t) = (251 rad/s)t - (20.4 rad/s^2)t^2 - (1.60 rad/s^3)t^3. At what time is the angular velocity of the motor shirt zero? Calculate the angular acceleration at the instant that the motor shaft has zero angular velocity. How many revolutions does the motor shaft turn through between the time when the current is reversed and the instant when the angular velocity is zero? How fast was the motor shaft rotating at t = 0, when the current was reversed?

Explanation / Answer

theta(t) = 251t -20.4t^2 -1.6*t^3

angular velocity is w = d(theta)/dt = (d/dt)(251t-20.4t^2-1.6t^3) = 251-(2*20.4*t)-(3*1.6*t^2)

required time when the angular velocity is zero is t

w= 0 rad/sec

then

0 = 251-(2*20.4*t)-(3*1.6*t^2)

t = 4.13 sec

B) angular accelaration is alpha = dw/dt = -(2*20.4) -(2*3*1.6*t)

at t = 4.13 sec

alpha = -(2*20.4) -(2*3*1.6*t)

alpha = -(2*20.4) -(2*3*1.6*4.13)

alpha = -80.448 rad/s^2

C) theta = 251t -20.4t^2 -1.6*t^3

theta = (251*4.13)-(20.4*4.13^2)-(1.6*4.13^3) = 576 rad

N = 576/(2*pi) = 576/(2*3.142) = 91.66 revolutions

so the answer is N = 91 rotations

D) w = 251-(2*20.4*t)-(3*1.6*t^2)

w = 251 rad/sec

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