Electric Ceiling Fan: 0.0988 Rev in 0.208s

In summary, to find the number of revolutions a ceiling fan has turned in a given time interval, we can use the formula theta(t) = theta(0) + w(0)t + 0.5at^2, where theta(0) is the initial angle, w(0) is the initial angular velocity, a is the angular acceleration, and t is the time interval. By using this formula, we can find the final angular velocity and then calculate the number of revolutions from there. Alternatively, we can use the method of finding the average velocity by taking the arithmetic average of the initial and final velocities, and then using that average angular velocity to find the number of revolutions. Both methods should yield the same answer.
  • #1
teenholiday
4
0

Homework Statement


An electric ceiling fan is rotating about a fixed axis with an initial angular velocity of 0.290 rev/s. The angular acceleration is 0.888 rev/s^2. Its blades form a circle of diameter 0.740 m.

Through how many revolutions has the blade turned in the time interval 0.208 s from Part A?

Homework Equations



theta (t) = theta (0) + w (0) t+ .5 at^2

The Attempt at a Solution



ngular velocity = .475 rev/ sec

.475 rev/s * .208 s = .0988 rev
 
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  • #2
Hi teenholiday,

teenholiday said:

Homework Statement


An electric ceiling fan is rotating about a fixed axis with an initial angular velocity of 0.290 rev/s. The angular acceleration is 0.888 rev/s^2. Its blades form a circle of diameter 0.740 m.

Through how many revolutions has the blade turned in the time interval 0.208 s from Part A?

Homework Equations



theta (t) = theta (0) + w (0) t+ .5 at^2

The Attempt at a Solution



ngular velocity = .475 rev/ sec

.475 rev/s * .208 s = .0988 rev


Why didn't you use the equation you have listed under "Relevant equations" in your post?

(In your work, you found the final velocity, and then you found the number of revolutions it would have taken if it had been rotating at that final velocity the entire time; but I don't think that is what's happening in this problem.)
 
  • #3
teenholiday said:

Homework Statement


An electric ceiling fan is rotating about a fixed axis with an initial angular velocity of 0.290 rev/s. The angular acceleration is 0.888 rev/s^2. Its blades form a circle of diameter 0.740 m.

Through how many revolutions has the blade turned in the time interval 0.208 s from Part A?

Homework Equations



theta (t) = theta (0) + w (0) t+ .5 at^2

The Attempt at a Solution



ngular velocity = .475 rev/ sec
How did you arrive at this? You were told that the initial angular velocity was .290 rev/s and the angular velocity is NOT a constant!

.475 rev/s * .208 s = .0988 rev
That is assuming a constant angular velocity which is not true. I'm with alphysicist: why not use the formula by have under "relevant equations"?

You could also use a different method: in general, with constant acceleration, the average velocity is just the arithmetic average of the initial velocity and the final velocity. You are told that the initial velocity is .475 rev/sec. It it accelerates at 0.888 rev per second per second for .208 seconds, how much will the angular velocity increase by? So what will be the final angular velocity? And then what is the average velocity? Using that average angular velocity, how many revolutions will be made in .208 seconds? You might try using both methods and see if you get the same answer.
 
  • #4
^^

thanks for the alternative method.

i had tried using the relevant equation, but i must have been tired or something, because i kept on getting the wrong answer.

i got it now though. thanks.
 

1. What does the measurement "0.0988 Rev" mean?

The measurement "0.0988 Rev" refers to the number of revolutions the ceiling fan makes in one second. This is also known as the rotational speed or the fan's revolutions per second (RPS).

2. What does the measurement "0.208s" refer to?

The measurement "0.208s" refers to the amount of time it takes for the ceiling fan to complete one revolution. This is also known as the fan's period or the time it takes for one complete cycle of rotation.

3. How is the rotational speed of a ceiling fan measured?

The rotational speed of a ceiling fan is typically measured by using a tachometer, which is a device that measures the speed of rotation. The tachometer has a sensor that detects the fan's movement and calculates the number of revolutions per second.

4. What is the significance of the rotational speed of a ceiling fan?

The rotational speed of a ceiling fan is important because it affects the amount of air movement and circulation in a room. A higher rotational speed means the fan is moving more air, while a lower rotational speed may not provide enough air circulation.

5. How does the rotational speed of a ceiling fan affect energy consumption?

The rotational speed of a ceiling fan can impact its energy consumption. A higher rotational speed may use more electricity, resulting in higher energy costs. However, it is important to note that the energy consumption of a ceiling fan also depends on other factors such as the size and design of the fan, as well as the speed and duration of use.

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