Homework Help is Here – Start Your Trial Now!
Science
Physics
(c) Find the acceleration vector ā(t). What direction does the acceleration vector point in? Hint: The acceleration is the time-derivative of the velocity.

(c) Find the acceleration vector ā(t). What direction does the acceleration vector point in? Hint: The acceleration is the time-derivative of the velocity.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
See similar textbooks
icon
Related questions
Question
An object is moving in a circle of radius 10 cm centered on the origin in the xy-plane at a constant speed of 5 m/s.
Transcribed Image Text:An object is moving in a circle of radius 10 cm centered on the origin in the xy-plane at a constant speed of 5 m/s.
(c) Find the acceleration vector \(\vec{a}(t)\). What direction does the acceleration vector point in? Hint: The acceleration is the time-derivative of the velocity.
Transcribed Image Text:(c) Find the acceleration vector \(\vec{a}(t)\). What direction does the acceleration vector point in? Hint: The acceleration is the time-derivative of the velocity.
Expert Solution
Step 1

Given: Radius of the circle is r = 10 cm

centered at origin (0, 0) and the linear velocity of the particle is 

v = 5 m/s Representing the circular motion in vector form:

                                               Physics homework question answer, step 1, image 1

c)

From the figure position vector of the particle at any time t  is 

r→(t) = xi^ +yj^                                                                            

Now the angular velocity of the particle is given by:

ω = vr=5 m/s0.1 m    = 50 rad/s

Angle of the particle at time twill be

θ = ωt

hence the position coordinates of the particle at this moment will be:

x = r cos(ωt)y = r sin(ωt)

then by equation 1 the position vector will be:

r→(t) = (r cos(ωt)i^ +(r sin(ωt))j^      =0.1{cos(50t)i^ + sin(50t)j^}

steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
College Physics
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON
SEE MORE TEXTBOOKS