# Solving Two Bugs on a Fan Homework Problem

• srjs8812

#### srjs8812

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.

Welcome to PF.

Pretty close, but don't skip the lecture.

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