Angular Speed of Fishing Line [SOLVED]

[rcmango]

[SOLVED] angular speed.

Homework Statement

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.
rad/s

Homework Equations

w = w0 + a*t

The Attempt at a Solution

I don't understand why i can't solve this with this kinematic equation. please help.

 

[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.

 

[rcmango]

theta = w* t

so, 2.6 = w(9.8)

= .27
okay so that's the radians i believe. Now what's next.

 

[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.

 

[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?

 

[hage567]

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

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

but, i believe this is the distance around the something?

Yes the circumference is the distance around the reel.

not sure how to use this to get the answer though.

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).

if i can find theta using this, then this must be the w in the equation i used?

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.

 

[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

to get 8.76 rad/s

thankyou for helping me.