# Rotational Dynamics and angle of theta

1. Oct 4, 2005

### jman1211

I tried to do this problem with related rates and calculus. We have not done physics with calculus, however. The other way I thought about was using the angular velocity of the board when the stick is taken away. I cannot seem to solve it though.

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))

The board is hinged to the table.

Any hints would be wonderful.

2. Oct 6, 2005

### mukundpa

Though I am not getting the problem clearly, I think you are missing the correct value of the velocity of the ball when it leaves the board, after that it is a projectile.

The potential energy lost is converted in to the kinetic energy, both rotational and translational. the total kinetic energy of a ball having pure rotation is given by (7/10)mv^2 not (1/2)mv^2, where v is the velocity of center of mass.