Approximate a fishing reel to be two solid disks, each of radius 4.7 cm and comb

Question

Approximate a fishing reel to be two solid disks, each of radius 4.7 cm and combined mass 0.61 kg which can rotate without friction. String (of negligible mass) is wrapped around the reel (between the disks) all the way to its edge (see Fig la). The fishing line is strung with bait and left at rest in the water. A fish then suddenly takes the bait and starts to applies a constant force of 2.6 N on the fishing line, pulling the reel counterclockwise. What is the angular acceleration of the fishing reel? Immediately after taking the bait, how much fishing line does the fish pull from the reel in 0.26 s? (Assume this time interval is short enough that radius of the fishing line wrapped around the reel does not appreciably change during it.) Suppose instead this fisherman had cast his bait much further out, so that the fishing line left on the reel was only halfway out to the edge (see Fig lb). If all else was the same, re-answer parts a & b.

Explanation / Answer

given data

r=4.7 cm
m=0.6kg
F=2.6 N

(a) What is the angular acceleration of the fishing reel?
The force produces the torque, which causes the reel to rotate counter clockwise.
Torque = Force * perpendicular distance (in meters)
Perpendicular distance = radius = 0.047 m
Torque = 2.6 * 0.047

Torque = I *
I for solid disk = ½ * mass * radius^2 = ½ * 0.6 * 0.047^2
Torque = ½ * 0.6 * 0.047^2 * = 2.6 * 0.047 =184.4 rad/s^2

(b) Immediately after taking the bait, how much fishing line does the fish pull from the reel in 0.26 s?
(Assume this time interval is short enough that radius of the fishing line wrapped around the reel does not appreciably change during it.)
Linear distance = ½ * a * t^2
Convert angular acceleration to linear acceleration.
a = * r = 184.4 * 0.047 = 8.668m/s^2

Linear distance = ½ * 8.668* 0.26^2 0.2929 meters

(c) Suppose instead this fisherman had cast his bait much further out, so that the fishing line left on the reel was only halfway out to the edge. If all else was the same, re-answer parts a & b.
Since the mass of the fishing line is negligible, the amount of fishing line on the reel does not affect the moment of inertia of the reel or the torque.
SO
The answers do not change

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