35.5 Contact Point of a Wheel Rolling Without Slipping

TL;DR

When a wheel rolls without slipping, the contact point between the wheel and the ground is instantaneously at rest.

Transcript

So I would like to now consider the wheel that is rolling without slipping. And what I'd like to do is consider-- let's draw the wheel rolling without slipping. And I'd like to consider the contact point between the wheel and the ground. And I'd like to understand what the velocity of that contact point is. And the result is surprising. Now, we kno... Read More

Key Insights

• 🧑‍🦼 The contact point between a wheel and the ground is instantaneously at rest when the wheel is rolling without slipping.
• 😥 The velocity of the contact point is the vector sum of the velocities of the wheel's center of mass and a point on the rim.
• 🤣 The magnitudes of these velocities are equal according to the rolling without slipping condition.

Questions & Answers

Q: How is the velocity of the contact point between the wheel and the ground calculated when the wheel is rolling without slipping?

The velocity of the contact point is the sum of the velocity of the wheel's center of mass and the velocity of a point on the wheel's rim in the center of mass frame. These velocities are equal in magnitude.

Q: What does it mean for the contact point to be instantaneously at rest with respect to the ground in rolling without slipping?

It means that the contact point's velocity is zero. This occurs because the magnitudes of the velocities of the wheel's center of mass and a point on the rim, in the center of mass frame, are equal.

Q: How does the velocity of a point on the rim change when the wheel is rolling without slipping?

When the wheel is rolling without slipping, the velocity of a point on the rim in the center of mass frame is in the opposite direction to the velocity of the center of mass. The magnitude of this velocity is equal to the radius of the wheel multiplied by the angular velocity.

Q: What is the significance of the contact point being instantaneously at rest with the ground in a wheel rolling without slipping?

The fact that the contact point is at rest with the ground is a key characteristic of a wheel rolling without slipping. It differentiates the motion of a wheel from that of other points on the wheel's rim or center of mass.

Summary & Key Takeaways

• The analysis focuses on the contact point between a wheel and the ground when the wheel is rolling without slipping.

• The velocity of the contact point is the vector sum of the velocity of the wheel's center of mass and the velocity of a point on the wheel's rim in the center of mass frame.

• The rolling without slipping condition states that the magnitudes of these two velocities are equal, resulting in the contact point being at rest with respect to the ground.