Question

Three particles A, B and C, each of mass m, are connected to each other by three massless rigid rods to form a rigid, equilateral triangular body of side l. This body is placed on a horizontal frictioness table (x-y plane) and is hinged to it at the point A so that it can move without friction about the vertical axis through A (see figure). The body is set into rotational motion on the table about A with a constant angular velocity ω.

(a) Find the magnitude of the horizontal force exerted by the hinge on the body.

(b) At time T, when the side BC is parallel to the x-axis, a force F is applied on B along BC (as shown). Obtain the x-component and the y-component of the force exerted by the hinge on the body, immediately after time T.

Answer 1

The mass B is moving in a circular path centred at A. The centripetal force (mlω2) required for this circular motion is provided by F′. Therefore a force F′ acts on A (the hinge) which is equal to mlω2 . The same is the case for mass C. Therefore the net force on the hinge is

(b) The force F acting on B will provide a torque to the system. This torque is

The total force acting on the system along x-direction is

F + (Fnet)x

This force is responsible for giving an acceleration ax to the system.