Angular Variables and Tangential Variables

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To determine the angular speed of the reel, the relationship between linear speed and angular speed is applied, where linear speed (v) equals the radius (r) multiplied by angular speed (ω). Given that the fishing line is wound onto the reel at a constant speed, the linear speed can be calculated by dividing the total distance of the line (2.6 m) by the time taken (8.4 s), resulting in a linear speed of approximately 0.3095 m/s. The radius of the reel is 3.0 cm, which converts to 0.03 m. Using the formula v = r * ω, the angular speed can be derived as ω = v/r, yielding an angular speed of approximately 10.32 rad/s. This calculation illustrates the relationship between linear and angular motion in the context of the fishing reel.
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In 8.4 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.
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If a disc spins, then the linear speed v of a pt on the circumference is given by v=r*w, where w(omega) is the angular speed of the disc.
 

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