How many revolutions did the fish make?

[Charlene]

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
alpha=(3.14rad/sec-0)/10sec
therefore, angular accelerate = .314 rad/sec^2

b.) .314rad/sec^2 *1rev/2pi rad = 0.50 revolutions around the rock.

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]

b.) .314rad/sec^2 *1rev/2pi rad = 0.50 revolutions around the rock.

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.

 

[Charlene]

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 shouldn't 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]

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.

 

[Charlene]

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

so i found this formula, 1/2*alpha*time^2
(.314 rad/sec^2)*(100 sec^2)*(.5)=15.7 rad *1rev/2pi rad = 2.50 revolutions

 

[mfb]

Right.