hw23_s - homework 23 YOO, HEE Due: Mar 25 2008, 4:00 am...

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homework 23 – YOO, HEE – Due: Mar 25 2008, 4:00 am 1 Question 1, chap 12, sect 2. part 1 of 1 10 points A large wheel is coupled to a wheel with half the diameter as shown. r 2 How does the rotational speed of the smaller wheel compare with that of the larger wheel? How do the tangential speeds at the rims compare (assuming the belt doesn’t slip)? 1. The smaller wheel has four times the ro- tational speed and the same tangential speed as the larger wheel. 2. The smaller wheel has twice the rotational speed and twice the tangential speed as the larger wheel. 3. The smaller wheel has twice the rotational speed and the same tangential speed as the larger wheel. correct 4. The smaller wheel has half the rotational speed and half the tangential speed as the larger wheel. Explanation: v = r ω The tangential speeds are equal, since the rims are in contact with the belt and have the same linear speed as the belt. The smaller wheel (with half the radius) rotates twice as fast: p 1 2 r P (2 ω ) = r ω = v Question 2, chap 12, sect 3. part 1 of 1 10 points A wheel rotating with a constant angular acceleration turns through 19 rev during a 7 s time interval. Its angular velocity at the end of this interval is 15 rad / s. What is the angular acceleration of the wheel? Note: The initial angular velocity is not zero. Correct answer: 0 . 58696 rad / s 2 (tolerance ± 1 %). Explanation: Let : N = 19 rev , t = 7 s , and ω = 15 rad / s . Total angle through which the wheel rotates for N revolutions is Δ θ = N 2 π = 119 . 381 rad Δ θ = ω 0 t + 1 2 αt 2 (1) ω ω 0 = αt, or ω 0 = ω α t, substituting into Eq . 1 Δ θ = ( ω αt ) t + 1 2 α t 2 , so α = 2 ω t Δ θ t 2 = 2 (15 rad / s) (7 s) (119 . 381 rad) (7 s) 2 = 0 . 58696 rad / s 2 . Question 3, chap 12, sect 3. part 1 of 3 10 points As a result of friction, the angular speed of a wheel changes with time according to dt = ω 0 exp ( σ t ) , where ω 0 and σ are constants. The angular speed changes from an initial angular speed of 3 . 19 rad / s to 2 . 32 rad / s in 10 . 6 s .
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homework 23 – YOO, HEE – Due: Mar 25 2008, 4:00 am 2 Hint: Use this information to determine σ and ω 0 . Determine the magnitude of the angular acceleration after 1 . 67 s. Correct answer: 0 . 0911469 rad / s 2 (tolerance ± 1 %). Explanation:
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hw23_s - homework 23 YOO, HEE Due: Mar 25 2008, 4:00 am...

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