Project ForgeA solid disc of radius r rolls without slipping on a horizontal floor with angular velocity ω and angular acceleration α. The magnitude of the acceleration of the point of contact on the disc is
- Azero
- Brα
- C√((rα)²+(rω²)²)
- rω²
Explanation
For rolling without slipping, the acceleration of the contact point has two horizontal (tangential) contributions — one from the center's own translational acceleration a_C=rα, and one from the angular acceleration acting through the radius vector to the contact point — and these two contributions are exactly equal and opposite, cancelling completely. What remains is only the centripetal component directed from the contact point toward the disc's center, of magnitude rω².
Source: GATE ME 2012 (Booklet Code A) (2012)
This question is part of a 15-day revision cycle — sign in and Project Forge will bring it back the day before you'd forget it.