How many revolutions did the fish make?

In summary: There you used a formula, and it's the right formula - although I can't quite follow the units you used. But the result is correct. In summary, the fish makes 2.50 revolutions around the rock after 10 seconds, given a constant angular acceleration of 0.314 rad/sec^2.
  • #1
Charlene
23
0

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.
 
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  • #2
Charlene said:
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.
 
  • #3
mfb said:
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?
 
  • #4
Charlene said:
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.
 
  • #5
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
 
  • #6
Right.
 

1. How do you determine the number of revolutions a fish has made?

The number of revolutions a fish has made can be determined by counting the number of times the fish's tail passes a fixed point. This can be done by recording the fish's movements with a high-speed camera and analyzing the footage to count the number of tail movements.

2. Can you estimate the number of revolutions a fish has made without using a high-speed camera?

Yes, it is possible to estimate the number of revolutions a fish has made by observing its movements and counting the number of tail movements. However, this method may not be as accurate as using a high-speed camera.

3. Do different types of fish make different numbers of revolutions?

Yes, different types of fish may make different numbers of revolutions depending on their size, shape, and swimming style. For example, a larger fish with a longer tail may make more revolutions than a smaller fish with a shorter tail.

4. Can the number of revolutions a fish makes change over time?

Yes, the number of revolutions a fish makes can change over time as the fish grows or if it changes its swimming style. Factors such as water temperature and food availability can also affect the number of revolutions a fish makes.

5. Is there a maximum number of revolutions a fish can make?

There is no specific maximum number of revolutions a fish can make as it depends on the individual fish's size and swimming style. However, larger and more active fish may make more revolutions compared to smaller and slower fish.

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