Need Help Understanding Cycloid Rolling vs Slipping

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In summary, the conversation discusses the difference between using the parametrization (sin(t)-t, cos(t)+1) and (sin(t)-at, cos(t)+1) for the cycloid curve, where a is not equal to 1. It is explained that the first parametrization causes the cycloid to roll while the second one causes it to slip. The conversation also provides a hint to understand this phenomenon by considering the distance the circle has gone and the distance it needs to go to avoid slipping.
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shoushou
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Hi everyone,
i have a problem concerning with the reason to why taking the cycloid to be parametrised by (sin(t)-t, cos(t)+1) causes it to roll, whereas taking (sin(t)-at, cos(t)+1) for a is not quals to 1, would cause it to slip.


can anybody explain to me or give me a hint, thanks a lot.
 
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Welcome to PF!

shoushou said:
Hi everyone,
i have a problem concerning with the reason to why taking the cycloid to be parametrised by (sin(t)-t, cos(t)+1) causes it to roll, whereas taking (sin(t)-at, cos(t)+1) for a is not quals to 1, would cause it to slip.

Hi shoushou! Welcome to PF! :smile:

Hint:

i] from each of the equations, how far has the circle gone when it completes a 360º revolution?

ii] how far does it need to go to avoid slipping?

iii] then prove it for smaller angles. :smile:
 

1. What is the difference between cycloid rolling and slipping?

Cycloid rolling and slipping refer to two different ways in which a rolling object moves. In cycloid rolling, the object rotates and moves forward without any sliding or slipping. In slipping, the object slides or skids as it moves forward.

2. How does an object roll in a cycloid motion?

In cycloid rolling, the object rotates around a fixed point on its circumference while moving in a straight line. This creates a cycloid shape, where the object's center of mass follows a curve while its point of contact with the ground remains stationary.

3. What causes an object to slip while rolling?

An object may slip while rolling due to factors such as insufficient traction, uneven surfaces, or external forces acting on the object. Friction also plays a role in preventing or causing slipping during rolling motion.

4. Can an object experience both cycloid rolling and slipping at the same time?

No, an object cannot experience both cycloid rolling and slipping at the same time. These are two distinct types of motion that cannot occur simultaneously. An object can transition from one type of motion to the other, depending on the external factors affecting its movement.

5. How is understanding cycloid rolling vs slipping useful in real-life scenarios?

Understanding cycloid rolling and slipping can be useful in various fields, including engineering, physics, and mechanics. It can help in designing and optimizing the movement of objects, such as wheels or gears, and predicting how they will behave under different conditions. It can also aid in solving problems related to friction and motion, such as in vehicle design and control.

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