# Angular speed.

1. Nov 23, 2007

### rcmango

[SOLVED] angular speed.

1. The problem statement, all variables and given/known data

In 9.8 s a fisherman winds 2.6 m of fishing line onto a reel whose radius is 3.0 cm (assumed to be constant as an approximation). The line is being reeled in at a constant speed. Determine the angular speed of the reel.

2. Relevant equations

w = w0 + a*t

3. The attempt at a solution

2. Nov 23, 2007

### hage567

He's reeling it at a constant speed, so there's no acceleration. Figure out how many radians the 3.0 cm radius reel goes through knowing that there is 2.6 m of line.

3. Nov 23, 2007

### rcmango

theta = w* t

so, 2.6 = w(9.8)

= .27
okay so thats the radians i believe. Now whats next.

4. Nov 23, 2007

### hage567

The equation you have there is the one you will use after you figure out theta. Make sure to check your units to see that they make sense when you do a calculation. What you have there is an answer in m/s, which isn't anything like radians.

There are 2*pi radians in one revolution (or in a circle). So you need to figure out how many times a length of 2.6 m can go around a circle of radius 3.0 cm. Do you know how to find the circumference of a circle?

Once you know that, you can find theta because you know how many times the string has gone around the reel, and you know how many radians there are in one trip around the reel.

5. Nov 23, 2007

### rcmango

alright circumference, is pi * 2r which is about 18.84

but, i believe this is the distance around the something?
not sure how to use this to get the answer though.
if i can find theta using this, then this must be the w in the equation i used?

6. Nov 23, 2007

### hage567

You need to change the 3.0 cm into meters. You have to keep your units consistent, keep track of them.

Yes the circumference is the distance around the reel.
So, if you have 2.6 m of line, and the circumference is 0.19 m, how many times can you wrap the line around before you don't have any left?

Then, for each wrap of the line around the reel, the angle you are going through is 2*pi radians (or 360 degrees). Multiply how many times you can go around the reel by 2*pi to get the total angular displacement (in radians).

I don't quite understand what this means, but the number I've described how to find is theta. w is what the problem has asked you to find. The units of w should be radians/second. Keep track of your units to see if you get that in the end.

7. Nov 23, 2007

### rcmango

thanks for the help with this problem, okay, i found 2.6/ .19 to get 13.68 times.

so then i divided that by 9.8