3:05 AM
1

When you hold a loose string by its two ends, and just let it dangle in space, it looks an awful lot like a parabola. I mean, on first sight, who wouldn't have thought that? It was only upon closer inspection that we realized in fact the shape formed is not a parabola, but a catenary (see the gra...

3 hours later…

14 hours later…
8:15 PM
6

For a rigid body rotating with a constant angular speed, the points near the axis must have lower linear velocity than the points farther away. If they have different linear velocities, they must have a non-zero relative velocity. If they have a non-zero relative velocity, the distance between th...

2 hours later…
9:53 PM
3

Q: An amusement park proprietor wishes to design a rollercoaster with a vertical circular loop in the track, of radius $R = 20\, \rm m$. Before the cars reach the loop, they descend from a maximum height h, at which they have zero velocity. Assuming the cars roll freely (no motor and no friction...