00:01
Okay, given two objects with the same mass and radius that are set down an incline from rest, which will reach the bottom first.
00:13
So the way we want to think about this is in terms of energy, and we also want to say that whichever object reaches the bottom with the fastest speed will reach the bottom first, right? so let's say you have two objects and they both reach the bottom at different times.
00:36
One reaches the bottom with a speed of 10 meters per second and one with a speed of 20 meters per second.
00:43
Well the one that reached the bottom with 20 meters per second speed will have reached first, right? you could show that through kinematics but we'll kind of accept that as just a basic fact here.
00:56
So whichever is fastest at the bottom reached first.
00:59
So now we apply conservation of energy.
01:04
Our initial energy here at the top, our final energy is here at the bottom.
01:10
So initially we have kinetic energy mghh, or sorry, potential energy, mghh.
01:16
At the bottom we have kinetic energy, one -half mv squared, plus one -half the moment of inertia, the angular speed squared.
01:25
So it's rotating, right? they're rolling.
01:30
So you have to include rotational inertia as well as linear or translational energy...