Answered: 2. When a taut string is unwound from a…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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2. When a taut string is unwound from a stationary cylinder, the end B of
the string generates a curve known as the involute of a circle. If
the string is unwound at the constant angular speed ω, the
equation of the involute is
? = ? ??? ?? + ??? ??? ?? ? = ? ??? ?? − ??? ??? ??
where R is the radius of the cylinder. Find the speed of B as a function of
time. Show that the velocity vector is always perpendicular to the string.

2. When a taut string is unwound from a stationary cylinder, the end B of
y
the string generates a curve known as the involute of a circle. If
the string is unwound at the constant angular speed w, the
equation of the involute is
B
Involute
String
x = R cos wt + Rwt sin wt
y = R sin wt – Rwt cos wt
A
R
where R is the radius of the cylinder. Find the speed of B as a function of
time. Show that the velocity vector is always perpendicular to the string.

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