hw28 - Muraj Hamza – Homework 28 – Due 4:00 am – Inst...

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Unformatted text preview: Muraj, Hamza – Homework 28 – Due: Apr 10 2006, 4:00 am – Inst: Florin 1 This print-out should have 11 questions. Multiple-choice 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 x-axes), 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 x-axis. 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 y-axis and ~g is into the page, in the figure below. Therefore the direction of the torque ~ τ is along the positive y-axis. + 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.

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hw28 - Muraj Hamza – Homework 28 – Due 4:00 am – Inst...

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