In 9.7 s a fisherman winds 2.1 m of fishing line onto a reel whose radius is 30 cm (assumed to be constant as an approximation).

The line is reeled in at constant speed.
Determine the angular speed of the reel in rad/s.
Thank you.

speed tangential=2.1/9.7 m/s

tangential speed= w*r

anglar speed=tangenital speed/radius

I'm still confused.

to find angular speed =
tnngenital speed/radius, would the radii cancel out, leaving only the tangential speed?

still confused as to set up

To determine the angular speed of the reel in radians per second, we need to use the formula for linear speed:

Linear speed = Angular speed × Radius

In this case, the linear speed is given by the distance covered divided by the time taken:

Linear speed = Distance / Time

The distance covered is 2.1 meters, and the time taken is 9.7 seconds. Substituting these values into the equation, we have:

Linear speed = 2.1 m / 9.7 s

Now, we need to find the radius of the reel in meters. The radius is given as 30 centimeters (cm), and to convert it to meters, we divide by 100:

Radius = 30 cm / 100 = 0.3 meters

Plugging in the values for distance and time, we have:

Linear speed = 2.1 m / 9.7 s
Radius = 0.3 m

Now, we can rearrange the linear speed formula to solve for angular speed:

Angular speed = Linear speed / Radius

Calculating the angular speed:

Angular speed = (2.1 m / 9.7 s) / 0.3 m

Dividing the numerator and denominator separately:

Angular speed = 2.1 m / (9.7 s * 0.3 m)

Simplifying the expression:

Angular speed = 2.1 m / 2.91 s

Finally, dividing the distance by the time:

Angular speed ≈ 0.721 rad/s

Therefore, the angular speed of the reel is approximately 0.721 radians per second.