Now pick it up
Think about dropping a pencil so the pencil makes an angle with the horizontal in the air but has no rotation. After the collision with the ground the pencil bounces up and starts to rotate around a horizontal axis. Find the angle the pencil should make with the horizontal in degrees so that the angular velocity of the pencil is maximum after the bounce.
Details and assumptions
- Treat the pencil as a rod with uniform mass distribution along its length.
- Assume there's no friction between the pencil and the floor and the collision is perfectly elastic.