Study guide and
2 practice problems
on:
Parameterization of complicated motions
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To parameterize a curve consisting of multiple types of motion (e.g. translation + rotation):
Describe the desired point as the vector sum of each part
Identify a convenient parameter. When in doubt, choose time
Find each part's dependence on the parameter
Related topics
Parameterized curves
(5 problems)
Multivariable calculus
(147 problems)
Lines, Planes, and Curves
(13 problems)
Practice problems
Consider a cylinder of radius $r$ rolling up a hill of incline $\theta$ at constant speed $v$. Initially the point of contact is $(0,0)$. Find the trajectory of the point initially contacting the hill.
Solution
A frisbee of radius $r$ translates rightward at speed $v$ meter/second. It rotates clockwise at $\omega$ radian/second. Initially the frisbee is centered at the origin.
Find the trajectory swept by the point initially at $(0,r)$.
Compute the speed as a function of time.
Describe when the speed is largest and smallest.
Solution