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Unformatted text preview: 19. Picture the Problem : The fish exerts a torque on the fishing reel and it rotates with constant angular acceleration. Strategy: Use Table 101 to determine the moment of inertia of the fishing reel assuming it is a uniform cylinder ( 2 1 2 MR ). Find the torque the fish exerts on the reel by using equation 111. Then apply Newton’s Second Law for rotation (equation 114) to find the angular acceleration and equations 102 and 1010 to find the amount of line pulled from the reel. Solution: 1. (a) Use Table 101 to find I : ( 29 ( 29 2 2 1 1 2 2 0.99 kg 0.055 m 0.0015 kg m I MR = = = × 2. Apply equation 111 directly to find : τ ( 29 ( 29 0.055 m 2.2 N 0.121 N m r F τ = = = × 3. Solve equation 1114 for : α 2 2 0.121 N m 81 rad/s 0.0015 kg m I τ α × = = = × 4. (b) Apply equations 102 and 1010: ( 29 ( 29 ( 29 ( 29 2 2 2 1 1 2 2 0.055 m 81 rad/s 0.25 s 0.14 m s r r t θ α = = = = Insight: This must be a small fish because it is not pulling very hard; 2.2 N is about 0.49 lb or 7.9 ounces of force. Or maybe the fish is tired? 26. Picture the Problem : The person lies on a lightweight plank that rests on two scales as shown in the diagram at right. Strategy: Write Newton’s Second Law in the vertical direction and Newton’s Second Law for rotation to obtain two equations with two unknowns, m and cm x . Solve each to find m and cm x . Using the left side of the plank as the origin, there are two torques to consider: the positive torque due to the right hand scale and the negative torque due to the person’s mass. Solution: 1. (a) Write Newton’s Second Law in the vertical direction to find m : 2. (b) Write Newton’s Second Law for rotation and solve for x cm : Insight: The equation in step 1 does not depend on the axis of rotation that we choose, but the equation in step 2 does. Nevertheless, we find exactly the same cm x if we choose the other scale,...
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 Spring '11
 BEAN
 Angular Momentum, Moment Of Inertia, Rotation, li, kg ×m

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