# How many revolutions did the fish make?

## Homework Statement

A fish starts at rest and uniformly accelerates. After 10 seconds, he is swimming around a rock at a rate of 3.14 rad/sec.
a.) What's the magnitude of angular acceleration?
b.) How many times did the fish circle the rock (how many revolutions?)

## Homework Equations

a.) wf=wi+alpha*t

## The Attempt at a Solution

a.)wf=wi+alpha*t
alpha=(wf-wi)/t
therefore, angular accelerate = .314 rad/sec^2

I just wanted to double check that i did part b correctly because i guess i'm having trouble seeing how the sec^2 on the bottom of the units end up disappearing to become just revolutions.

mfb
Mentor
Where does that calculation come from? It is wrong. As you noted, the units don't match - and you did not use the time here, which is another sign that something is wrong.

Where does that calculation come from? It is wrong. As you noted, the units don't match - and you did not use the time here, which is another sign that something is wrong.
well all i did was use the conversion to convert rad to rev, i didn't use any type of formula, so perhaps i shouldnt be using the angular acceleration in part b?
should i just take the 3.14 rad/sec and multiply it by the 10 secs to get 31.4 rad and then divide by 2pi to get around 5.00 revolutions?

mfb
Mentor
should i just take the 3.14 rad/sec and multiply it by the 10 secs to get 31.4 rad and then divide by 2pi to get around 5.00 revolutions?
No, that would assume a constant angular velocity.

If you start at rest on a street with a constant linear acceleration of 4 m/s2, how far do you go within 10 seconds?
For rotations the situation is nearly the same.

oh okay, i see that i need to include the angular acceleration.

so i found this formula, 1/2*alpha*time^2