Problem # p036

Determine angular momentum

A thin rod OA of negligible mass is attached to a rod rotating about the origin 0 in the xy plane with an angular speed of 25 rpm at the instance when it arrives on the x-axis as shown. Simultaneously, the 2 kg sphere is sliding along the rod 0A away from the origin with a speed of 2 m/s.

Determine the following quantities :
  1. The x- and y-component of the velocity of the sphere in the position shown in the figure.
  2. The angular momentum of the sphere with respect to the origin 0.
  3. 1 second after the position shown in the above figure the rod with the sphere has rotated a bit in clock-wise direction around point 0 and the distance between the sphere and the origin 0 of the coordinate system has increased to 1.6 m. How big is the angular velocity now, assuming that there are no external forces acting on the rod + sphere ?