Explanation Refer to figure P10.74; consider that air resistance has a negligible affect on a drop so that mechanical energy is conserved in the drop-Earth system. The first drop leaving the wheel has a velocity v 1 directed upward. Write the expression for first drop velocity when it comes off the wheel as. K i = U f (I) Here, K i is initial kinetic energy and U f is final potential energy. Write the expression for initial kinetic energy as. K i = 1 2 m v 1 2 Here, m is the mass of bicycle and v 1 is the velocity of first turn. Write the expression for final potential energy as. U f = m g h 1 Here, g is acceleration under gravity and h 1 is height reached by drop in the first turn. Substitute 1 2 m v 2 for K i and m g h 1 for U f in equation (I) 1 2 m v 2 = m g h 1 Simplify the above equation for velocity as. v 1 = 2 g h 1 (II) Write the expression for velocity for second turn as. v 2 = 2 g h 2 (III) Here, v 2 is the velocity of second turn at height reaches by drop to h 2 . Write the expression for angular speed for first turn as. ω 1 = v 1 r Here, ω 1 is angular speed of first turn. Write the expression for angular speed for second turn as. ω 2 = v 2 r Here, ω 2 is the angular speed for second turn and r is the radius of turn. Write the expression for angular acceleration as. α = ω 2 2 − ω 1 2 2 θ Here, α is the angular acceleration and θ is the angular distance

Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 9th + WebAssign Printed Access Card, Multi-Term

9th Edition

ISBN: 9781305932302

Author: Raymond A. Serway, John W. Jewett

Publisher: Cengage Learning

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Definition Definition Rate of change of angular velocity. Angular acceleration indicates how fast the angular velocity changes over time. It is a vector quantity and has both magnitude and direction. Magnitude is represented by the length of the vector and direction is represented by the right-hand thumb rule. An angular acceleration vector will be always perpendicular to the plane of rotation. Angular acceleration is generally denoted by the Greek letter α and its SI unit is rad/s 2 .

Chapter 10, Problem 74AP

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The magnitude of the average angular acceleration of the wheel.

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Chapter 10, Problem 73AP

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Chapter 10 Solutions

Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 9th + WebAssign Printed Access Card, Multi-Term

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