Question

Problem 1 (25 points): The figure below shows a uniform beam of mass M = 3 kg and length L = 1 m (I_{com} = 1/12 ML^2) which makes angle theta = 30° with respect to the horizontal. The beam is attached to a rotation axis at a distance d = 0.2 m from one end and is supported by a vertical wire at the other end. The beam is initially in static equilibrium. a) (6 points) Draw the forces (on the figure) which act on the beam. b) (7 points) Find the tension T in the wire, and the components Fx and Fy of the force applied by the rotation axis. c) (6 points) If the wire is cut, find the initial angular acceleration alpha of the beam. d) (6 points) Find the angular velocity omega of the beam when it has dropped to the horizontal (theta = 0°) position. Also find the magnitude of the velocity v of the right end of the beam at this moment.

          Problem 1 (25 points):
The figure below shows a uniform beam of mass M = 3 kg and length L = 1 m (I_{com} = 1/12 ML^2) which makes angle theta = 30° with respect to the horizontal. The beam is attached to a rotation axis at a distance d = 0.2 m from one end and is supported by a vertical wire at the other end. The beam is initially in static equilibrium.
a) (6 points) Draw the forces (on the figure) which act on the beam.
b) (7 points) Find the tension T in the wire, and the components Fx and Fy of the force applied by the rotation axis.
c) (6 points) If the wire is cut, find the initial angular acceleration alpha of the beam.
d) (6 points) Find the angular velocity omega of the beam when it has dropped to the horizontal (theta = 0°) position. Also find the magnitude of the velocity v of the right end of the beam at this moment.

Problem 1 (25 points):
The figure below shows a uniform beam of mass M = 3 kg and length L = 1 m (Icom = 1/12 ML^2) which makes angle theta = 30° with respect to the horizontal. The beam is attached to a rotation axis at a distance d = 0.2 m from one end and is supported by a vertical wire at the other end. The beam is initially in static equilibrium.
a) (6 points) Draw the forces (on the figure) which act on the beam.
b) (7 points) Find the tension T in the wire, and the components Fx and Fy of the force applied by the rotation axis.
c) (6 points) If the wire is cut, find the initial angular acceleration alpha of the beam.
d) (6 points) Find the angular velocity omega of the beam when it has dropped to the horizontal (theta = 0°) position. Also find the magnitude of the velocity v of the right end of the beam at this moment.

Added by Gonzalo L.

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