Physics, 26.07.2019 18:30 Dancy31uv

An electric fan is turned off, and its angular velocity decreases uniformly from 720 rev/min to 200 rev/min in a time interval of length 3.25 a. find the angular acceleration in rev/s b. find the number of revolutions made by the motor in the time interval of length 3.25 c. how many more seconds are required for the fan to come to rest if the angular acceleration remains constant at the value calculated in part a?

Answers: 1

Show answers

Answers

An electric fan is turned off, and its angular velocity decreases uniformly from 720 rev/min to 200 rev/min in a time interval of length 3.25. The angular acceleration is 2.67 rev/s². The angular displacement θ = 26.99 rev. The time required for the fan to come to rest if the angular acceleration remains constant is 4.5 seconds.

The angular acceleration which is also known as rotational acceleration is the change of angular velocity with time.

$\mathbf{angular \ acceleration \ \alpha = \dfrac{\omega - \omega_o}{\Delta t} }$

1 rev/min = 2 π/60 rad/s²

∴

$\mathbf{angular \ acceleration \ \alpha = \dfrac{200 \times (\dfrac{2 \pi}{60}) - 720 \times (\dfrac{2 \pi}{60}) }{3.25} }$

$\mathbf{angular \ acceleration \ \alpha = \dfrac{20.94395102- 75.39822369 }{3.25} }$

$\mathbf{angular \ acceleration \ \alpha = \dfrac{-54.45427267 }{3.25} }$

$\mathbf{angular \ acceleration \ \alpha =-16.755 \ rad/s^2 \times (\dfrac{1}{2 \pi })}$

$\mathbf{angular \ acceleration \ \alpha =2.67 \ rev/s^2}$

The angular displacement refers to the number of revolutions made by the motor which can be computed as:

$\mathbf{angular \ displacement \ \theta = \dfrac{\omega^2 - \omega_o^2}{2 \alpha} }$

$\mathbf{angular \ displacement \ \theta = \dfrac{200 \times ((\dfrac{2 \pi}{60}))^2 - (720 \times (\dfrac{2 \pi}{60}))^2 }{2(-16.755)} }$

$\mathbf{angular \ displacement \ \theta = 169.58 \ rad/s }$

angular displacement θ = 26.99 rev

The time required for the fan to come to rest if the angular acceleration remains constant is calculated by using the formula:

$\mathbf{ \Delta \ t = \dfrac{\omega - \omega_o}{\alpha} }$

$\mathbf{ \Delta \ t = \dfrac{0 - 720 (\dfrac{2\pi}{60})}{-16.755} }$

$\mathbf{ \Delta \ t = 4.5 \ seconds }$

Therefore, we can conclude that the angular acceleration is 2.67 rev/s². The angular displacement θ = 26.99 rev. The time required for the fan to come to rest if the angular acceleration remains constant is 4.5 seconds

Learn more about angular acceleration here:

link

Answer from: Kuwillalean38

(a) first, we need to convert the initial and final angular speed into rev/s. Keeping in mind that 1 min=60 s, we should divide the speeds by 60:
$\omega_i = 720 rev/min = 12.0 rev/s$
$\omega_f = 200 rev/min = 3.3 rev/s$

So, the angular acceleration is
$\alpha = \frac{\omega_f-\omega_i}{\Delta t} = \frac{3.3 rev/s - 12.0 rev/s}{3.25 s}=-2.68 rev/s^2$
where the negative sign means it is a deceleration.

(b) The angle covered by the fan (in revolutions) is given by the following equation
$\theta(t) = \omega_i t + \frac{1}{2} \alpha t^2$
where t is the time and $\alpha$ the angular acceleration we find at point (a). Substituting numbers, we get
$\theta (3.25 s)=(12.0 rev/s)(3.25 s)+ \frac{1}{2} (-2.68 rev/s^2)(3.25 s)^2=24.85 rev$

(c) In order for the fan to come to rest, its final angular speed must go to zero:
$\omega(t)=0$

The expression for the angular speed as a function of time is
$\omega(t) = \omega _i + \alpha t$
By requiring this is equal to zero, we find the time t after which the fan comes to rest:
$\omega_i + \alpha t = 0$
$t=- \frac{\omega_i}{\alpha}= -\frac{12.0 rev/s}{-2.68 rev/s^2} =4.48 s$

Answer from: Quest

the total distance traveled by the car is

30km + 49km = 79 km .

Answer from: Quest

Bag of bolts weight 29.4n

Another question on Physics

Physics, 22.06.2019 01:00

An object is 10 cm from the mirror, its height is 1 cm and the focal length is 5 cm. what is the image height? (indicate the object orientation by including the + or - sign with the answer.) hi = cm +1 -1 +10 -10

Answers: 3

Answer

Physics, 22.06.2019 04:10

Unpolarized light of intensity so passes through two sheets of polarizing material whose transmission axes make an angle of 60∘ with each other as shown in the figure. what is the intensity of the transmitted beam, st?

Answers: 3

Answer

Physics, 22.06.2019 19:50

State the below theories and give the name of the writer of the theory 1. wave theory 2. quantum theory 3. corpuscular theory 4. electromagnetic theory

Answers: 1

Answer

Physics, 22.06.2019 21:30

Ineed this now one scientist feels that the changes in global climatic patterns may be good for the health of the biosphere. another scientist feels that sharp changes in climatic patterns could result in the extinction of the biosphere. which of these is the most likely reason the two scientists gave conflicting opinions on the impact of changes in the global climatic pattern? they do not have enough knowledge on the topic. they did not discuss the issue among themselves. they believe conflicting opinion strengthens science. they study different areas of science and have different scientific focuses.

Answers: 1

Answer

You know the right answer?

An electric fan is turned off, and its angular velocity decreases uniformly from 720 rev/min to 200...

Questions