Solving Two Bugs on a Fan Homework Problem

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In summary, the conversation discusses a problem assigned by a professor on angular velocity and acceleration. The problem involves two bugs holding onto a spinning fan blade and asks questions about their angular acceleration, velocity, tangential acceleration, and displacement. The equations for solving the problem were not given, so the person attempts to solve it using their understanding of the relationships between these quantities. They conclude that the angular accelerations of both bugs are equal, the angular velocity is the same once the fan reaches its maximum speed, and bug B has a greater tangential acceleration and angular displacement due to its larger radius. They also mention the importance of attending lectures for a better understanding of the topic. However, they also question the inconsistency between some of their answers.
  • #1
srjs8812
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Here's a problem my professor assigned and expects us to know, yet he hasn't covered any of this material. We just started talking about angular velocity, acceleartion, etc. I understand that we are supposed to gather the relationships between these things by looking at the equations, but I keep going back and forth between some of my answers. I've done a search on google and scoured the pages of my book, but neither have very clear answers.

Homework Statement


Two bugs are honding onto a fan blade as it starts spinning. Bug A is half-way between the middle and outer edge of the blade while Bug B is holding onto the outer edge. The fan is turned on and takes 3 seconds to reach its maximum rotational speed of 120 rpm.

a. Which bug has the greater angular acceleration while the fan blade is gaining speed?
b. Which bug has a greater angular velocity during the first minute after the blade has reached its maximum rotational speed?
c. Which bug has a greater tangential acceleration while the fan blade is gaining speed?
d. Which bug has a greater tangential acceleration during the minute after the blade has reached its maximum rotational speed?
e. Which bug has a greater angualr displacement while the fan blade is gaining speed?
f. Which bug has a greater angualr displacement during the first minute after the blade has reached its maximum rotational speed?


Homework Equations



He didn't give us any equations, for the problem.



The Attempt at a Solution



a. Their angular accelerations are equal. Even though the radius is different between the bugs, they accelerate with the fan as a whole at the same rate.
b. After the blade has reached its maximum rotational speed, the angular velocity is the same b/c angular acceleration is zero.
c. Bug b has the greater tangential acceleration while the fan is speeding up. This is the first I've ever seen this phrase, and googling it, I think tangential acceleration depends on radius, and bug b has the greater radius.
d. After the blade has reached its maximum speed, angular acceleration is zero, so the tangential acceleration is also zero, so they are the same.
e. Bug B has the greater angular displacement b/c the radius from the center to Bug B is twice the size of the radius from the center to Bug A.
f. bug B has the greater angular displacement after the fan has reached its maximum speed for the same reason as before.
 
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  • #2
Welcome to PF.

Pretty close, but don't skip the lecture.

Isn't the answer in b) inconsistent with e) and f) ?
 
  • #3


Dear student,

I understand your frustration with this problem and your professor's lack of coverage on the relevant material. I would suggest approaching this problem by first understanding the fundamental concepts of angular velocity, acceleration, and displacement. These are all related to the rotational motion of objects, which in this case, is the fan blade.

To answer the first question, it is important to note that angular acceleration is defined as the rate of change of angular velocity. In other words, it is the change in rotational speed over time. Both Bug A and Bug B are experiencing the same angular acceleration as they are attached to the same fan blade, which is accelerating at a constant rate. Therefore, the answer to part a is that both bugs have the same angular acceleration.

Moving on to part b, it is important to understand that angular velocity is the measure of how fast an object is rotating, and it is given by the formula ω = θ/t, where ω is angular velocity, θ is angular displacement, and t is time. After the fan has reached its maximum rotational speed, the angular acceleration becomes zero, and therefore, the angular velocity remains constant. This means that both bugs will have the same angular velocity during the first minute after the blade has reached its maximum speed.

In regards to tangential acceleration, it is defined as the rate of change of tangential velocity. Tangential velocity is the linear velocity at a point on a rotating object, and it is given by the formula v = rω, where v is tangential velocity, r is the radius, and ω is the angular velocity. From this equation, we can see that tangential acceleration depends on both tangential velocity and radius. In this problem, Bug B has a greater radius, and therefore, it will have a greater tangential acceleration while the fan blade is gaining speed. However, after the blade has reached its maximum speed, the tangential acceleration becomes zero for both bugs, so they will have the same tangential acceleration during the first minute.

For part e, angular displacement is the angle through which an object has rotated, and it is given by the formula θ = ωt, where θ is angular displacement, ω is angular velocity, and t is time. Bug B is attached to the outer edge of the fan blade, which means it will have a greater angular displacement compared to Bug A, which is attached to a point closer to the center. This
 

1. What is the "Two Bugs on a Fan" homework problem?

The "Two Bugs on a Fan" homework problem is a common physics problem that involves two bugs crawling on a fan blade and their respective speeds and directions of motion.

2. How do I solve the "Two Bugs on a Fan" homework problem?

To solve the "Two Bugs on a Fan" homework problem, you will need to use principles of circular motion and relative velocity. You will also need to draw a diagram and apply relevant equations, such as the Law of Cosines and the Law of Sines.

3. What are the common mistakes to avoid when solving the "Two Bugs on a Fan" homework problem?

Common mistakes to avoid when solving the "Two Bugs on a Fan" homework problem include not considering the direction of motion, not using the correct equations, and not accurately representing the relative velocities of the bugs.

4. What are the key steps to solving the "Two Bugs on a Fan" homework problem?

The key steps to solving the "Two Bugs on a Fan" homework problem are: 1) drawing a diagram to represent the situation, 2) identifying the relevant equations, 3) considering the direction of motion, 4) applying the equations to find the unknown variables, and 5) checking your final answer for accuracy.

5. How can I check my work when solving the "Two Bugs on a Fan" homework problem?

You can check your work by using different methods, such as calculating the relative velocity in a different direction or using the Pythagorean Theorem to verify the magnitude of the relative velocity. Additionally, you can plug in your final answer to the original equations to see if they are satisfied.

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