VDU_Physics_1_010

# ## Physics 1.-  Mechanics:  Torque & Rotation

Javier Montenegro Joo

## jmj@VirtualDynamics.Org

### Torque and Rotation.-

 A circular disk of 2 kg and 1m diameter rotates about a perpendicular axis passing through its center. Determine the necessary torque to accelerate the disk from 0  to 500 rpm in 10 s.

Solution.- Two blocks of 15 kg and 30 kg are placed each at the extreme of a 1m massless bar. Next the system rotates at 30 rpm around an axis passing perpendicular to the bar at 25 cm of the lightest block. Determine the rotational kinetic energy of the system.

Solution.- Determine the radius of a 30-kg circular disk, bearing in mind that it must have the same moment of inertia of a 12-kg and 0.5-m length bar, whose rotation axis passes perpendicular to the bar through its mid-point.

Solution.- (4) A cylindrical rod of 5 kg and 20 cm diameter is initially at rest and it can freely rotate around its longitudinal axis. An inextensible rope of negligible mass is wrapped around the rod and pulls it  with a force of 20 N. Assuming the rope does not slip, determine: (a) The torque exerted by the applied force on the rod (b) the angular acceleration acquired by the rod (c) the angular velocity of the rod after 2 s.   Radius of gyration of the rod:     Rod Rg = R Sqrt(2) / 2

Solution.- (5) In order to slow down a rotating disk of radius R and mass M, the tip of a bar is radially pushed against the edge of the disk with a force Fo.  The coefficient of kinetic friction between the bar and the disk is Uk and, the disk is rotating with angular velocity Wo. Determine how long will it take for the pushing bar to stop the rotation of the disk.     Moment of inertia of the disk:    Idisk = MR²/2

Solution.-

The disk stops its rotation because of the frictional force between it and the bar pushing it. The frictional force exerts a torque against the rotation of the disk. The figure shows the disk rotating clockwise and the applied force pushing on radially from the left, the figure also shows the direction of the resulting frictional force between the bar and the disk. Libro sobre Caos escrito por Javier Montenegro Joo .-    Anatomía del Caos:   Estudio del Caos en modelos matemáticos, basado en Física Computacional y Simulacional: 