Question

In 8.4 s a fisherman winds 2.9 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.

Answer 1

Answer:

The angular speed of the reel is 11.33 rad/s

Explanation:

Given

The fisherman takes t = 8.4 s to wind distance x = 2.9 m into a circle radius of r = 3 cm = 0.03 m

Than the tangencial speed equals the change in the distance to the time

v = $\frac{x}{t}$ = $\frac{2.9 m}{8.4 s} = 0.34 \frac{m}{s}$

Knowing the tangencial velocity is proportional to the radius r and the angular velocity

v = r*w

w = $\frac{0.34 m/s}{0.03 m} = 11.33 \frac{rad}{s}$