A community for students.
Here's the question you clicked on:
 0 viewing
nightwill
 2 years ago
Can someone please explain why the cycloid curve has a vertical movement on the cusps? Thank you!
nightwill
 2 years ago
Can someone please explain why the cycloid curve has a vertical movement on the cusps? Thank you!

This Question is Closed

hellow
 2 years ago
Best ResponseYou've already chosen the best response.1As far as I understand it. . . the instantaneous direction of motion is vertical because the tangent to the graph of the motion at the cusp is vertical. Direction: The vertical tangent is explained in both the lecture (using approximations) and the Related Reading (using calculus). The slope (dy/dx) of the tangent to the curve signifies the direction of the curve, which in this case is the direction of motion. So the instantaneous direction of motion is vertical. Velocity: However, the Related Reading explains that the velocity of the point at the cusp is 0. So, the point has no instantaneous movement at the cusp (v=change in position/change in time=0). (We have position\[OP=<x,y>=<a \thetaasin \theta, aacos \theta>\]. So \[velocity =d(OP)/d \theta=<aacos \theta,asin \theta>\] which at the cusp is\[<aacos0, asin0>=<0,0>.)\] So at the cusp, the direction of motion is vertical, while the instantaneous velocity is 0.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.