35.4 Rolling Without Slipping Slipping and Skidding  Summary and Q&A
TL;DR
A comprehensive analysis of different conditions for a rolling wheel, including rolling without slipping, slipping, and skidding.
Key Insights
 đ¤Ŗ A rolling wheel can be in three different conditions: rolling without slipping, slipping, or skidding.
 đ§âđĻŧ Rolling without slipping occurs when the arc length a point on the wheel has moved is equal to the distance the wheel moves.
 đ Slipping happens when the wheel spins faster than it translates.
 đ Skidding occurs when the wheel slides along the ground faster than it spins.
 đ The velocity of the center of mass determines the conditions of slipping and skidding.
 đ Rolling without slipping is characterized by Vcm = RĪ, where Vcm is the velocity of the center of mass and RĪ is the tangential velocity relative to the center of mass.
 đ In slipping, RĪ > Vcm, while in skidding, Vcm > RĪ.
Transcript
Let's now consider our rolling wheel, and we want to look at some special conditions. So at time t equals 0 and we'll have our wheel that's rolling, here's the ground let's say that our point P is right up here at the top. That's cm. And we'll be in the ground frame now. And then at a later time, time t, the wheel has moved to the right. So let... Read More
Questions & Answers
Q: What is rolling without slipping?
Rolling without slipping is when the arc length a point on the wheel has moved is exactly equal to the distance the wheel has moved along the ground. This condition is indicated by Vcm = RĪ, where Vcm is the velocity of the center of mass and RĪ is the tangential velocity relative to the center of mass.
Q: What determines if a wheel is slipping?
If the arc length a point on the wheel has moved is greater than the distance the center of mass has moved, the wheel is slipping. This condition is represented by RĪ > Vcm, indicating that the wheel is spinning faster than it is translating.
Q: What is the skidding condition?
In the skidding condition, the wheel is not spinning but sliding horizontally. This occurs when the horizontal distance the center of mass has moved is greater than the amount of arc length that a point on the wheel has moved. The condition is Vcm > RĪ.
Q: How does the velocity of the center of mass relate to the sliding and spinning of the wheel?
In the slipping condition, the wheel is spinning faster than it is translating, resulting in RĪ > Vcm. In the skidding condition, where the wheel is sliding along the ground, Vcm > RĪ. These conditions indicate the relative speeds of spinning and translating of the wheel.
Summary & Key Takeaways

The analysis focuses on a rolling wheel and its position at different times.

It explores the relationship between the distance the wheel moves and the angle at which a point on the wheel has moved.

Three conditions are discussed: rolling without slipping, slipping (spinning faster than translating), and skidding (translating faster than spinning).