Chapter 7 Skill Building

Chapter 7 Skill Building - MasteringPhysics: Assignment...

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MasteringPhysics: Assignment Print View Uniform Circular Motion Learning Goal: To find the velocity and acceleration vectors for uniform circular motion and to recognize that this acceleration is the centripetal acceleration. Suppose that a particle's position is given by the following expression: . Part A Choose the answer that best completes the following sentence: The particle's motion at can be described by ____________. ANSWER: an ellipse starting at time on the positive x axis an ellipse starting at time on the positive y axis a circle starting at time on the positive x axis a circle starting at time on the positive y axis The quantity is defined to be the angular velocity of the particle. Note that must have units of radians per second. If is constant, the particle is said to undergo uniform circular motion . Part B When does the particle first cross the negative x axis? Express your answer in terms of some or all of the variables , , and . ANSWER: = Now, consider the velocity and speed of the particle. Part C
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MasteringPhysics: Assignment Print View Find the particle's velocity as a function of time. Part C.1 Part not displayed Express your answer using unit vectors (e.g., + , where and are functions of , , , and ). ANSWER: = Part D Find the speed of the particle at time . Hint D.1 Hint not displayed Part D.2 Part not displayed Express your answer in terms of some or all of the variables , , and . ANSWER: Note that the speed of the particle is constant: . Part E Now find the acceleration of the particle. Express your answer using unit vectors (e.g., + , where and are functions of , , , and ). ANSWER: = Part F
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MasteringPhysics: Assignment Print View Your calculation is actually a derivation of the centripetal acceleration. To see this, express the acceleration of the particle in terms of its position . Express your answer in terms of some or all of the variables , , , and . ANSWER: = Part G Now find the magnitude of the acceleration as a function of time. Express your answer in terms of some or all of the variables , , and . ANSWER: = Part H Finally, express the magnitude of the particle's acceleration in terms of and using the expression you obtained for the speed of the particle. Express your answer in terms of one or both of the variables and . ANSWER: = There are three important things to remember about centripetal acceleration: 1. The centripetal acceleration is simply the acceleration of a particle going around in a circle. 2. It has magnitude of either or . 3. It is directed radially inward. Centripetal Acceleration Explained
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MasteringPhysics: Assignment Print View Learning Goal: To understand that centripetal acceleration is the acceleration that causes motion in a circle.
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This note was uploaded on 01/26/2011 for the course PHYS 570 taught by Professor Davids.king during the Fall '10 term at Caltech.

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Chapter 7 Skill Building - MasteringPhysics: Assignment...

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