Book edition 9th Edition

Author(s) Raymond A. Serway, John W. Jewett

Pages 1624 pages

ISBN 9781133947271

Answers without the blur.

Just sign up for free and you're in.

Short Answer

A small object with mass 4.00 kg moves counter-clockwise with constant angular speed 1.50 rad/s in a circle of radius 3.00 m centered at the origin. It starts at the point with position vector $3.00 \hat{i} m$ . It then undergoes an angular displacement of 9.00 rad. (a) What is its new position vector? Use unit-vector notation for all vector answers. (b) In what quadrant is the particle located, and what angle does its position vector make with the positive x axis? (c) What is its velocity? (d) In what direction is it moving? (e) What is its acceleration? (f) Make a sketch of its position, velocity, and acceleration vectors. (g) What total force is exerted on the object?

The new position vector of object is $(- 2.74 \hat{i} + 1.22 \hat{j}) m$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Identification of given data

The mass of object is m = 4 kg

The constant angular speed of object is $ω = 1.50 r a d / s$

The radius of circle is R = 3m

The angular displacement of object is $δ = 9 r a d$

Step 2: Conceptual Explanation

The angular speed of an object is the rate of variation of the angular displacement of the object with time.

Step 3: Determination of new position vector

The angle for the new position vector is given as:

$α = δ (\frac{180 °}{π}) - 360 = (9 r a d) (\frac{180 °}{π r a d}) - 360 ° = 156 °$

The new position vector of object is given as:

$\vec{r} = R (\cos α \hat{i} + \sin α \hat{j}) = (3 m) [(\cos 156 °) \hat{i} + (\sin 156 °) \hat{j}] = (- 2.74 \hat{i} + 1.22 \hat{j}) m$

Therefore, the new position vector of object is $(- 2.74 \hat{i} + 1.22 \hat{j}) m$ .

Find Study Materials for

Create Study Materials

Select your language

Physics For Scientists & Engineers

Answers without the blur.

Short Answer

Step by Step Solution

Step 1: Identification of given data

Step 2: Conceptual Explanation

Step 3: Determination of new position vector

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Select your language

Physics For Scientists & Engineers

Answers without the blur.

Short Answer

Step by Step Solution

Step 1: Identification of given data

Step 2: Conceptual Explanation

Step 3: Determination of new position vector

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Work Energy and Power

Radiation

Astrophysics

Physics of Motion

Scientific Method Physics

Fluids

Torque and Rotational Motion

Nuclear Physics

Fields in Physics

Measurements

Space Physics

Electricity

Physical Quantities and Units

Medical Physics

Electrostatics

Further Mechanics and Thermal Physics

Mechanics and Materials

Engineering Physics

Energy Physics

Force

Particle Model of Matter

Waves Physics

Magnetism

Modern Physics

Atoms and Radioactivity

Dynamics

Electricity and Magnetism

Conservation of Energy and Momentum

Fundamentals of Physics

Kinematics Physics

Circular Motion and Gravitation

Linear Momentum

Rotational Dynamics

Oscillations

Translational Dynamics

Geometrical and Physical Optics

Thermodynamics

Magnetism and Electromagnetic Induction

Electromagnetism

Electric Charge Field and Potential

Turning Points in Physics