Old Midterm 03 - sanchez(ds28677 oldmidterm 03 Turner(58220...

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sanchez (ds28677) – oldmidterm 03 – Turner – (58220) 1 This print-out should have 24 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points A rotating bicycle wheel has an angular speed of 56 / s at 4 . 6 s and a constant angular acceleration of 21 / s 2 . With the center of the wheel at the origin, the valve stem is on the positive x -axis (horizontal) at t 0 = 1 . 4 s. Through what angle has the valve stem turned between 1 . 4 s and 8 . 5 s? Correct answer: 449 . 785 . Explanation: Let : ω 1 = 56 / s , t 1 = 4 . 6 s , α = 21 / s 2 , θ 0 = 0 , t 0 = 1 . 4 s , and t = 8 . 5 s . The initial angular velocity can be deter- mined from ω 1 = ω 0 + α ( t 1 t 0 ) ω 0 = ω 1 α ( t 1 t 0 ) = 56 / s (21 / s 2 ) (4 . 6 s 1 . 4 s) = 11 . 2 / s . This θ 2 = ω 0 ( t 2 t 0 ) + 1 2 α ( t 2 t 0 ) 2 = ( 11 . 2 / s) (8 . 5 s 1 . 4 s) + 1 2 (21 / s 2 ) (8 . 5 s 1 . 4 s) 2 = 449 . 785 . 002 (part 1 of 3) 10.0 points A beetle takes a joy ride on a pendulum. The string supporting the mass of the pendulum is 190 cm long. If the beetle rides through a swing of 49 , how far has he traveled along the path of the pendulum? Correct answer: 162 . 49 cm. Explanation: Let : r = 190 cm , and θ = 49 . Arc length is defined as s = r θ = (190 cm)(49 ) · parenleftBig π 180 parenrightBig = 162 . 49 cm . 003 (part 2 of 3) 10.0 points What is the displacement experienced by the beetle while moving theough the same angle 49 ? Correct answer: 157 . 583 cm. Explanation: Using the law of cosines, we have bardbl vector R bardbl = radicalbig r 2 + r 2 2 r r cos θ = r radicalbig 2 (1 cos θ ) = (190 cm) radicalbig 2(1 cos 49 ) = 157 . 583 cm . Alternative Solution: Divide the isosce- les triangle in half. Then bardbl vector R bardbl = 2 . 0 r sin parenleftbigg θ 2 parenrightbigg = 2 . 0 (190 cm) sin 24 . 5 = 157 . 583 cm . 004 (part 3 of 3) 10.0 points If the pendulum at some instant is swinging at 1 . 7 rad / s, how fast is the beetle traveling? Correct answer: 323 cm / s. Explanation:
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sanchez (ds28677) – oldmidterm 03 – Turner – (58220) 2 Let : ω = 1 . 7 rad / s . Linear and angular velocity are related by v = r ω = (190 cm)(1 . 7 rad / s) = 323 cm / s . keywords: 005 10.0 points At t = 0, a wheel rotating about a fixed axis at a constant angular deceleration of 0 . 66 rad / s 2 has an angular velocity of 2 . 7 rad / s and an angular position of 6 . 5 rad. What is the angular position of the wheel after 3 s? Correct answer: 11 . 63 rad. Explanation: Let : α = 0 . 66 rad / s 2 , ω 0 = 2 . 7 rad / s , θ 0 = 6 . 5 rad , and t = 3 s . The angular position is θ f = θ 0 + ω 0 t + 1 2 α t 2 = 6 . 5 rad + (2 . 7 rad / s) (3 s) + 1 2 ( 0 . 66 rad / s 2 ) (3 s) 2 = 11 . 63 rad . 006 10.0 points A massless rod of length L has a small mass m fastened at its center and another mass m fastened at one end. On the opposite end from the mass m , the rod is hinged with a frictionless hinge. The rod is released from rest from an initial horizontal position; then it swings down. What is the angular velocity as the rod swings through its lowest (vertical) position?
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