Question

During startup of a power plant, a turbine accelerates from rest at 0.58 rad/s2 .

1-How long does it take to reach its 2600 rpm operating speed? Express your answer using two significant figures

2-How many revolutions does it make during this time?Express your answer using two significant figures.

Answer 1

1.

w_o = initial angular speed = 0 rad/s

w_f = final angular speed = 2600 rpm = 2600 (2pi/60) = 272.13 rad/s

t = time taken = ?

$\alpha$ = angular acceleration = 0.58

using the equation

w_f = w_o + $\alpha$ t

272.13 = 0 + (0.58) t

t = 469.2 sec

2)

$\theta$ = angular displacement = w_o t + (0.5) $\alpha$ t² = (0) (469.2) + (0.5) (0.58) (469.2)² = 6.4 x 10⁴

n = number of revolution = $\theta$/2pi = (6.4 x 10⁴)/(2 x 3.14) = 1.02 x 10⁴ revolution