1. A cycloid is the curve traced by a point on a circle as it rolls along a straight line without slipping.(т, 2R)Rt27 RIf the radius of the circle is R and its center at a moment t has coordinates (Rt, R), then cycloidis parameterized as follows:r(t) = R(t – sint, 1cos t),0

Given a cycloid parametric equation : r(t)=R<t-sin t, 1-cos t>, 0≤t≤2π We need to find…

A cycloid is the curve traced by a point on a circle as it rolls along a straight line without slipping. Y (T, 2R) Rt 2т R If the radius of the circle is R and its center at a moment t has coordinates (Rt, R), then cycloid is parameterized as follows: r(t) = R(t – sin t, 1 – cos t), 0

A cycloid is the curve traced by a point on a circle as it rolls along a straight line without slipping. Y (T, 2R) Rt 2т R If the radius of the circle is R and its center at a moment t has coordinates (Rt, R), then cycloid is parameterized as follows: r(t) = R(t – sin t, 1 – cos t), 0

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.

Question

1. A cycloid is the curve traced by a point on a circle as it rolls along a straight line without slipping.
(т, 2R)
Rt
27 R
If the radius of the circle is R and its center at a moment t has coordinates (Rt, R), then cycloid
is parameterized as follows:
r(t) = R(t – sint, 1
cos t),
0<t< 27.
(a) Find parametric equation of the tangent line to cycloid at a point r(to), 0 < to < 2m.
(b) (Descartes' theorem) Show that the tangent line to cycloid at a point P is perpendicular to
the line PQ, where Q is the point of the contact of the circle and the baseline (see figure
below).
P
(c) Find the length of the arc of cycloid between r(t1) and r(t2), where 0 < ti < t2 < 2T. What
is the length of the complete arc? Hint: if needed, your TA will remind you of some useful
trigonometric identities.

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