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Get Full Access to Calculus - 8 Edition - Chapter 13 - Problem 1
Get Full Access to Calculus - 8 Edition - Chapter 13 - Problem 1

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# A particle P moves with constant angular speed around a ISBN: 9781285740621 127

## Solution for problem 1 Chapter 13

Calculus | 8th Edition

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A particle P moves with constant angular speed around a circle whose center is at the origin and whose radius is R. The particle is said to be in uniform circular motion. Assume that the motion is counterclockwise and that the particle is at the point sR, 0d when t 0. The position vector at time t > 0 is rstd R cos t i 1 R sin t j. (a) Find the velocity vector v and show that v ? r 0. Conclude that v is tangent to the circle and points in the direction of the motion. (b) Show that the speed | v | of the particle is the constant R. The period T of the particle is the time required for one complete revolution. Conclude that T 2R | v | 2 (c) Find the acceleration vector a. Show that it is proportional to r and that it points toward the origin. An acceleration with this property is called a centripetal acceleration. Show that the magnitude of the acceleration vector is | a | R2 . (d) Suppose that the particle has mass m. Show that the magnitude of the force F that is required to produce this motion, called a centripetal force, is | F | m| v | 2 R

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1/25/2017 Homework #1 • It must be completed on-line in McGraw Hill Connect. • Accessible after 5:00 p.m., January 26. • Closes at noon, February 7. • No deadline extension is allowed. • No discussion on the homework questions is allowed. • Chapters 1 through 3 covered. • Ten multiple-choice questions,10 points each. • You are allowed to re-do and re-submit it until the closing date. • Every time you submit it, you can find out what your total score is. • On-line signing up for Connect will close on January 31. GEOL 1303-003, Spring 2017 1 Igneous Rocks, Intrusive Activity, and the Origin of Igneous Rocks Physical Geology 15/e,

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##### ISBN: 9781285740621

This full solution covers the following key subjects: particle, show, acceleration, motion, Vector. This expansive textbook survival guide covers 16 chapters, and 250 solutions. This textbook survival guide was created for the textbook: Calculus, edition: 8. Since the solution to 1 from 13 chapter was answered, more than 285 students have viewed the full step-by-step answer. Calculus was written by and is associated to the ISBN: 9781285740621. The full step-by-step solution to problem: 1 from chapter: 13 was answered by , our top Calculus solution expert on 11/10/17, 05:27PM. The answer to “A particle P moves with constant angular speed around a circle whose center is at the origin and whose radius is R. The particle is said to be in uniform circular motion. Assume that the motion is counterclockwise and that the particle is at the point sR, 0d when t 0. The position vector at time t > 0 is rstd R cos t i 1 R sin t j. (a) Find the velocity vector v and show that v ? r 0. Conclude that v is tangent to the circle and points in the direction of the motion. (b) Show that the speed | v | of the particle is the constant R. The period T of the particle is the time required for one complete revolution. Conclude that T 2R | v | 2 (c) Find the acceleration vector a. Show that it is proportional to r and that it points toward the origin. An acceleration with this property is called a centripetal acceleration. Show that the magnitude of the acceleration vector is | a | R2 . (d) Suppose that the particle has mass m. Show that the magnitude of the force F that is required to produce this motion, called a centripetal force, is | F | m| v | 2 R” is broken down into a number of easy to follow steps, and 216 words.

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