Physics, 27.11.2019 05:31 jennyferluna0216

Acooling fan is turned off when it is running at 850 rev/min. it turns 1500 revolutions before it comes to a stop. (a) what was the fan's angular acceleration, assumed constant? (b) how long did it take the fan to come to a complete stop?

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Answer from: donbright100

The fan's angular acceleration assumed constant is -0.42rad/s²

The time it takes the fan to come to a complete stop is 211.90secs

In order to get the fan's angular acceleration, we will use the equation of rotation is expressed as:

ω² = ω₀² + 2 α θ where;

ω is the final angular velocity

ω₀ is the initial angular velocity

α is the angular acceleration

θ is the angle

Since the body comes to rest, hence ω = 0

θ = 1500 x 2 x π

θ = 9424.78 rad

Since the cooling fan revolution is 850rev/min, the final angular velocity will be 89 rad/s

Substitute the given parameters to get the angular acceleration

$0 = 89^2 + 2 \times \alpha \times 9424.78\\-7921=18,849.56\alpha\\\alpha=\frac{-7921}{18849.56}\\\alpha= -0.42rad/s^2$

b) Next is to get the time it takes for the fan to stop

$\omega = \omega_0+\alpha t\\0=89-0.42t\\0.42t=89\\t=\frac{89}{0.42}\\t= 211.90secs$

Hence the time it takes the fan to come to a complete stop is 211.90secs

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Answer from: ultimatesaiyan

The angular acceleration of fan is $-16.58 \;\rm rad/s^{2}$ .

The fan will take 5.36 seconds to stop completely.

Given data:

The number of rotation made by fan per minute is, $N = 850 \;\rm rpm$ .

The number of revolutions is, n = 1500 .

(a)

The angular displacement made by the fan is,

$\theta = \dfrac{n}{2 \pi} \\\theta = \dfrac{1500}{2 \pi}\\\theta = 238.73 \;\rm rad$

And, angular speed at initial is,

$\omega_{i}=\dfrac{2\pi N}{60} \\\omega_{i}=\dfrac{2\pi \times 850}{60}\\\omega_{i}=89 \;\rm rad/s$

Now, apply the third rotational equation of motion as,

$\omega^{2}_{f}=\omega^{2}_{i}+2 \alpha \theta\\0^{2}=89^{2}+2 \times \alpha \times 238.73\\\alpha =-16.58 \;\rm rad/s^{2}$

Thus, the angular acceleration of fan is $-16.58 \;\rm rad/s^{2}$ .

(b)

Applying the first rotational equation of motion to obtain the time taken to stop as,

$\omega_{f}=\omega_{i}+\alpha t\\0= 89+(-16.58) t\\t = 5.36 \;\rm s$

Thus, the fan will take 5.36 seconds to stop completely.

Learn more about the rotational equation of motion here:

link

Answer from: Quest

Is a vector quantity that refers to "the rate at which an object changes its position." imagine a person moving rapidly - one step forward and one step back - always returning to the original starting position. while this might result in a frenzy of activity, it would result in a zero velocity. because the person always returns to the original position, the motion would never result in a change in position. since velocity is defined as the rate at which the position changes, this motion results in zero velocity. if a person in motion wishes to maximize their velocity, then that person must make every effort to maximize the amount that they are displaced from their original position. every step must go into moving that person further from where he or she started. for certain, the person should never change directions and begin to return to the starting position.

Answer from: Quest

answer: 2×10^-2kg

explanation: density= mass per volume

vol=mass/density

converting to s.i units we have;

3÷1000kg = 0.003

1.5÷100m = 0.15

0.003/0.15 = 0.02kg

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