Calculating Revolutions in 1.0 s with Given Tension and Moment of Inertia

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The problem involves calculating the number of revolutions a fishing reel makes when a fish creates a tension of 65 N in the line. The torque is calculated as 2.6 N·m, leading to an angular acceleration of 650 rad/s² based on the reel's moment of inertia of 4.0 x 10^-3 kg·m². The initial calculation mistakenly focused on angular velocity instead of the angular displacement (theta). Upon reevaluation, the correct answer for the number of revolutions in 1.0 s is determined to be 52 revolutions. This highlights the importance of correctly identifying the parameters needed for rotational motion calculations.
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Problem:
A large fish strikes bait cast by a fisherman with a rod
and reel. The fish creates tension in the line of 65 N.
How many revolutions of the reel occur in 1.0 s if the
reel has a moment of inertia of 4.0 * 10^-3 kg-m2 and the
radial distance of the line from the reel’s axis is 4.0
cm? Assume the reel has negligible friction.


Solution:

calculated Torque from tension force: 65N*.04m = 2.6

ƩTorque = I*(angular Acceleration)
2.6/ ( 4.0 10^-3) = angular Acceleration = 650

(650)*(1sec) = Angular Velocity = 650 rad/sec * rev/(2pi) = 103 rev/sec.

What am I doing wrong? the answer is 52 rev
 
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Sorry... I just realized what I did wrong... I solved for ang velocity instead of theta...
 
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