# Rotational Dynamics of a light cup

1. Dec 10, 2008

### asura

1. The problem statement, all variables and given/known data

A common physics demonstration consists of a ball resting at the end of a board of length L that is elevated at an angle of theta with the horizontal. A light cup is attached to the board at Rc (Rc is a distance up the board from the bottom, it is not past the support stick) so that it will catch the ball when the support stick is suddenly removed. a) show that the ball will lag behind the falling board when theta < 35.3 and b) the ball will fall into the cup when the board is supported at this limiting angle and the cup is placed at
Rc = (2L)/(3cos$$\theta$$)

2. Relevant equations

$$\alpha$$r = a
x = vot + .5at2

3. The attempt at a solution

The ball falls straight down from the end of the board, so I found the time that it takes with x = vot + .5at2 .Next I wanted to find the time it takes for the beam (and cup) to fall down, but I'm not sure how to do this. I tried using a component of gravity (gcos$$\theta$$) as the tangential acceleration, but then I realized that this value changes as the beam falls. So, how do I approach this problem?

2. Dec 11, 2008

### Staff: Mentor

Start by finding the angular acceleration of the stick as a function of angle.