Question

the operating angular speed of a motor is 4000rpm. starting from rest it takes 2 minutes to reach that speed. how many revolutions does it take to reach the operating speed?

Answer 1

Hi there!

Begin by solving for the angular acceleration using the following:

$\large\boxed{\omega_f = \omega_i + \alpha t}$

ωf = final angular velocity (4000 rpm)

ωi = initial angular velocity (0 rpm)

α = angular acceleration (r/m²)

t = time (min)

Solve:

$4000 = 2\alpha\\\alpha = 2000 rpm^2$

Now, we can use the rotational kinematic equation:

$\large\boxed{\omega_f^2 = \omega_i^2 + 2\alpha \theta}}$

Plug in the known values:

$4000^2 = 0 + 2(2000) \theta\\\\16000000 = 4000\theta\\\\\theta = \large\boxed{4000 rev}$

Answer 2

Starting from rest, the motor accelerates smoothly to 4000 rpm.

The average speed of the motor during that time is. 1/2 (0 + 4000) = 2000 rpm.

At the average speed of 2000 rpm, the motor will turn 2•(2000 rpm) in 2 minutes.

That's 4,000 revolutions.