Question

The blades of a fan running at low speed turn at 26.2 rad/s. When the fan is switched to high speed, the rotation rate increases uniformly to 36.5 rad/s in 5.75 seconds. What is the magnitude of the fan's angular acceleration

Answer 1

Answer: $1.79\ rad/s^2$

Explanation:

Given

Initial angular speed is $\omega_1=26.2\ rad/s$

Final angular speed is $\omega_2=36.5\ rad/s$

Time period $t=5.75\ s$

Magnitude of the fan's acceleration is given by

$\Rightarrow \alpha=\dfrac{\omega_2-\omega_1}{t}$

Insert the values

$\Rightarrow \alpha=\dfrac{36.5-26.2}{5.75}\\\\\Rightarrow \alpha=\dfrac{10.3}{5.75}\\\\\Rightarrow \alpha=1.79\ rad/s^2$

Thus, fan angular acceleration is $1.79\ rad/s^2$

Answer 2

Answer:

The angular acceleration is given by 1.8 rad/s^2.

Explanation:

initial angular speed, wo = 26.2 rad/s

final angular velocity, w = 36.5 rad/s

time, t = 5.75 seconds

The first equation of motion is

$w = wo + \alpha t\\\\36.5 = 26.2 + 5.75\alpha\\\\\alpha = 1.8 rad/s^2$