   Chapter 12.3, Problem 47E

Chapter
Section
Textbook Problem

# Circular Motion In Exercises 47-50, consider a particle moving on a circular path of radius b described by r ( t ) = b cos ω t i + b sin ω t j where ω = d u / d t is the constant angular speed.Find the acceleration vector and show that its direction is always toward the center of the circle.

To determine

To calculate: The acceleration vector of a particle which is moving on a circular path of radius b is r(t)=bcosωti+bsinωtj where ω=du/dt and then show that its direction is toward the center of the circle.

Explanation

Given:

The provided particle path is r(t)=bcosωti+bsinωtj.

Formula used:

The acceleration vector is:

a(t)=v(t).

Calculation:

Consider the position vector,

r(t)=bcosωti+bsinωtj

Differentiate position vector with respect to t gives a velocity vector,

v(t)= r(t)=(bωsinωti+bωcosωtj)

Differen

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