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(t)=( 255 rad/s )t( 19.0 rad/s2 )t2( 1.50 rad/s3 )t3.

Part A

At what time is the angular velocity of the motor shaft zero?

Part B

Calculate the angular acceleration at the instant that the motor shaft has zero angular velocity.

Part C

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?

Part D

How fast was the motor shaft rotating at t=0, when the current was reversed?

Part E

Calculate the average angular velocity for the time period from t=0 to the time calculated in part A.

Explanation / Answer

A)Theta = 255 t - 19.3 t^2 -1.45 t^3
W = d(theta)/dt = 255- 38.6 t - 4.35 t^2 = 0
Re-arrange and divide by 4.35 t0 get t^2 + 8.87 t - 58.6 = 0
t= 4.41 s

b) Alpha = dW/dt =-38.6 -8.70 t  
When t = 4.41,   

Alpha = -38.8 - 8.7x 4.41 = - 77 rad/s^2  

c) Theta (at t= 4.41) =

255 (4.41) - 19.3 (4.41)^2 - 1.45 (4.41)^3
= 627 Radians x 1 rev/2pi radians

= 99.8 rev

D)58.82-0.977-0.0175=57.8755

E)W = d(theta)/dt = 255/4.41

=57.82rad/s

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