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Unformatted text preview: Muraj, Hamza – Homework 28 – Due: Apr 10 2006, 4:00 am – Inst: Florin 1 This printout should have 11 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 3 kg bicycle wheel rotating at a 2799 rev / min angular velocity has its shaft supported on one side, as shown in the figure. When viewing from the left (from the positive xaxes), one sees that the wheel is rotating in a clockwise manner. The distance from the center of the wheel to the pivot point is 0 . 4 m. The wheel is a hoop of radius 0 . 4 m, and its shaft is horizontal. Assume all of the mass of the system is located at the rim of the bicycle wheel. The acceleration of gravity is 9 . 8 m / s 2 . y z x . 4 m mg ω 2 7 9 9 r e v / m i n ω . 4 m radius Find the change in the precession angle after a 1 . 9 s time interval. Correct answer: 9 . 09936 ◦ . Explanation: Let : m = 3 kg , ω = 2799 rev / min = 2 π (2799 rev / min) (60 s / min) = 293 . 111 rad / s , b = 0 . 4 m , and R = 0 . 4 m . Basic Concepts: ~ τ = d ~ L dt Solution: The magnitude of the angular momentum I of the wheel is L = I ω = mR 2 ω , and is along the negative xaxis. From the figure in Part 2, we get Δ φ = Δ L L . Using the relation, Δ L = τ Δ t, where τ is the torque, ~ τ = ~ b × m~g . The precession angle Δ φ is Δ φ = Δ L L = τ Δ t L = mg b Δ t mR 2 ω = g b Δ t R 2 ω = (9 . 8 m / s 2 ) (0 . 4 m) (1 . 9 s) (0 . 4 m) 2 (293 . 111 rad / s) = 0 . 158814 rad = 9 . 09936 ◦ . ~ τ = ~ b × m~g , where ~ b is along the positive yaxis and ~g is into the page, in the figure below. Therefore the direction of the torque ~ τ is along the positive yaxis. + x x L + Δ L Δ L Δ φ Δ L τ wheel Viewed from Above + y L We can see the direction of precession is clockwise, due to ~ τ =→ Δ L Δ t , that is Δ L is in the direction of the torque τ and is producing clockwise motion ( ~ L × ~ τ produces clockwise motion). 002 (part 1 of 2) 10 points Muraj, Hamza – Homework 28 – Due: Apr 10 2006, 4:00 am – Inst: Florin 2 A uniform brick of length 14 m is placed over the edge of a horizontal surface with the maximum overhang x possible without falling....
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This note was uploaded on 04/12/2010 for the course PHY 58195 taught by Professor Turner during the Spring '09 term at University of Texas.
 Spring '09
 Turner

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