Chapter_10_solved_problem - Chapter 10 solved problems NOTE...

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Chapter 10 solved problems NOTE: A few of the problems here have slightly different numerical values than in the book but the solution is the correct one with the values given here. 8. Picture the Problem : The Earth rotates once on its axis every 24 hours. Strategy: Convert the known angular speed of 1 rev/day into units of radians per second. Solution: Convert the units: Insight: This angular speed corresponds to about 15° / hour. A “rule of thumb” in astronomy is that the “fixed” stars will move across the sky at this rate (1° every 4 minutes, or 15 arcsec/s) due to Earth’s rotation. 19 . Picture the Problem : The ceiling fan rotates about its axis, slowing down with constant angular acceleration before coming to rest. Strategy: Use the kinematic equations for rotation (equations 10-8 through 10-11) to find the number of revolutions through which the fan rotates during the specified intervals. Because the fan slows down at a constant rate of acceleration, it takes exactly half the time for it to slow from 0.90 rev/s to 0.45 rev/s as it does to come to a complete stop. Solution: 1. (a) Apply equation 10-9 directly: ( 29 ( 29 ( 29 1 1 0 2 2 0 0.90 rev/s 2.2 min 60 s min 59 rev t θ ϖ ϖ = + = + × = 2. (b) Apply equation 10-9 directly: ( 29 ( 29 ( 29 1 1 0 2 2 0.45 0.90 rev/s 1.1 min 60 s min 45 rev t θ ϖ ϖ = + = + × = Insight: An alternative way to solve the problem is to use equation 10-8 to find 2 0.0068 rev/s α = - and use α in equation 10-11 to find θ for each of the specified intervals. Note that you can stick with units of rev/s 2 to find θ in units of revolutions instead of converting to radians and back again. 24. Picture the Problem : The compact disk rotates about its axis, increasing its angular speed at a constant rate.
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