This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Thevalingam, Donald – Homework 29 – Due: Apr 27 2007, midnight – Inst: Eslami 1 This printout should have 16 questions. Multiplechoice questions may continue on the next column or page – find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points A wheel rotates about a fixed axis with an initial angular velocity of 77 rad / s. During a 6 s interval the angular velocity increases to 117 rad / s. Assume: The angular acceleration was con stant during this time interval. How many revolutions does the wheel turn through during this time interval? Correct answer: 92 . 6282 . Explanation: First find α α = ω f ω i Δ t = 6 . 66667 rad / s 2 . The total angle rotated in time t = 6 s is given by θ = ω t + 1 2 αt 2 = (77 rad / s)(6 s) + 1 2 (6 . 66667 rad / s 2 )(6 s) 2 = 582 rad . Finally, the number of revolutions rotated is simply N = θ 2 π = 92 . 6282 . keywords: 002 (part 1 of 1) 10 points A wheel starts from rest at t = 0 and rotates with a constant angular acceleration about a fixed axis. It completes the first revolution in 8 . 7 s. How long after t = 0 will the wheel com plete the second revolution? Correct answer: 12 . 3037 s. Explanation: In the conventional notation θ = s r ω = dθ dt = v r α = dω dt = a t r , we use “ θ θ = ω t + 1 2 αt 2 ” at time t 1 to find the acceleration. The wheel starts from rest ( ω = 0) θ 1 = 0 + 1 2 αt 2 1 ⇒ α = 2 θ 1 t 2 1 = 0 . 166024 rad / s 2 . If we use the same equation again at time t 2 θ 2 = 0 + 1 2 αt 2 2 ⇒ t 2 = r 2 θ 2 α = s 2 θ 2 t 2 1 2 θ 1 = r θ 2 θ 1 t 1 = √ 2 t 1 , because we know θ 2 = 2 θ 1 (two revolutions). Notice that the result does not depend on how many revolutions the wheel went through, only the relative number of revolutions θ 2 θ 1 ....
View
Full
Document
This note was uploaded on 03/04/2010 for the course PHY 303K taught by Professor Turner during the Spring '08 term at University of Texas at Austin.
 Spring '08
 Turner
 Physics, Work

Click to edit the document details