Question

The propeller of an aircraft accelerates from rest with an angular acceleration a = 3t + 9, where alpha is in rad/s^2 and t is in seconds. What is the angle in radians through which the propeller rotates from t = 1.00 s to t = 5.90 s?

Answer 1

here,

angular acceleration, alpha = (3*t + 9)

angular velocity, dw/dt = int(alpha) ( int is integration)
int(dw/dt) = int(3*t + 9)
w = 3x(x+6)/2

Angular displacement, Theta/dt = int(angular velocity) from t = 1s to t2 = 5.9 s
int(Theta/dt) = int(w)
int(Theta/dt) = int(3x(x+6)/2) from t = 1s to t2 = 5.9 s
Theta = 0.5*x^3 + 9.2x^2 + C from t = 1s to t2 = 5.9 s
Theta = (x^2( x + 9 )/ 2) from t = 1s to t2 = 5.9 s
Theta = 254.334 radians