Rotation without Translation

Question

So when a body rolls, it’s quite intuitive that its COM translates. But is it possible for the periphery of a disc to roll when its COM is at rest?

When we apply the brakes and try to accelerate a car, it stays at rest but the wheels rotate. What does the free body diagram look like for such a case?

Yes - think about spinning a basketball on your finger (or someone else doing that!) — Quantum Mechanic, Jun 20 '21 at 02:41
Or maybe a CD turning in a CD player. Are you asking about the free body diagram for the car or for the wheels? — Quantum Mechanic, Jun 20 '21 at 02:43
No, aren’t the cds and basket balls in context rotating about an axis? So obviously there isn’t any translational motion. My question is specifically about wheels on a road — user13387446, Jun 20 '21 at 02:45

score 1 · Answer 1 · answered Jun 20 '21 at 06:09

In a pure rolling condition, rolling without slipping where static friction between the wheel and the road is maintained, the COM does translate. In the situation where there is kinetic friction between the wheel and the road, then it is possible to have rotation of the wheel without translation of the COM. The case of the car with the brakes on spinning the tire without moving is an example of tire rotation. Rolling is defined as rotation and translation. You may want to see; https://en.wikipedia.org/wiki/Rolling

score 1 · Answer 2 · answered Jun 20 '21 at 06:29

What does the free body diagram look like for such a case?

Kinetic friction acts on the drive wheels that are spinning, and this acts in the forward direction. However, static friction on the wheels that are held still by the brakes acts in the opposite direction. If the static friction equals the kinetic friction then the car stays still. Once the kinetic friction exceeds the static friction, the car moves forward.

If the car is not held on its brakes then there is no (or at least very little) static friction acting on the non-drive wheels - they are free to roll along the ground. Then the friction from the drive wheels moves the car forward.

Rotation without Translation

2 Answers2