Question

a fan is rotating in 90 rpm,it is then switched off .it stops after 21 revolution
calculate the time to stop as the fricitional torque is constant

Answer 1

Answer in attachment

Explanation:

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Answer 2

Answer:

The time taken to stop the fan is 28 s.

Explanation:

The frequency of the fan is 90 rpm,

$f_0=\frac{90}{60}=1.5rps$

We will use the following equations to solve this question,

$\alpha=\frac{\omega-\omega_o}{t}$         (1)

$\alpha=\frac{\omega^2-\omega_o^2}{2\theta}$       (2)

Where,

α=angular acceleration

ω=final angular velocity

ω₀=initial angular velocity

θ=angular velocity=2π×number of revolution

From the question we have,

ω=0                (as the fan is switched off)

Number of revolution=21

Then,

$\theta=2\pi\times 21=42\pi$     (3)

$\omega_0=2\pi\f_0=2\pi\times1.5=3\pi$ (4)

From equations (1) and (2) we have,

$\frac{\omega-\omega_o}{t}=\frac{\omega^2-\omega_o^2}{2\theta}$         (5)

By placing the values of θ,ω, andω₀ in the above equation (5) we get;

$\frac{0-3\pi}{t}=\frac{0^2-(3\pi)^2}{2\times 42\pi}$

$t=28s$

Hence, the time taken to stop the fan is 28 s.