The tangential acceleration component of a point moving on R(1) = (cost +tsint)i +(sintt -rcost)j, is:

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 18T
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The tangential acceleration component of a point moving
on R(1) = (cost +tsint)i +(sintt -rcost)j,
is:
Transcribed Image Text:The tangential acceleration component of a point moving on R(1) = (cost +tsint)i +(sintt -rcost)j, is:
Expert Solution
Step 1

Given that, 

R(t)=(cos t + t sin t ) i +( sin t - t cos t )j

Step 2

The tangential acceleration component of a moving point is given by,

aT=R('t).R"(t)|R'(t)|---- (1)

Differentiating R(t) with respect to,

R'(t)=ddt[ (cos t + t sin t ) i + (sin t - t cos t )j]

R'(t)=ddt[ (cos t + t sin t )i] +ddt[ (sin t - t cos t )j]

R'(t)=[-sin t + 1. sin t + t cos t] i + [ cos t - 1. cos t + -(-sin t ) t ]

R'(t)=t cos t i + t sin t j ---- (2)

 

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