User:Sneha007/Torsional pendulum

A "Torsional pendulum" consists of a disc-like mass suspended from a thin wire. When the mass is twisted about the axis of the wire, the wire exerts a torque on the mass, tending to rotate it back to its original position. Such a back and forth oscillation executes simple harmonic motion. This gives us an idea of moment of inertia.

Analysis
A mass suspended to a fixed support by a thin wire can be made to twist about its axis. This is known as a torsional pendulum. The mass attached to the wire rotates in the horizontal plane. In this case θ is the angle of rotation. When the wire is untwisted and in equilibrium, the angle θ is 0 degrees. It is the twisting of the wire that creates a restoring torque due to the resistance of the wire to the deformation. For small angles of θ the magnitude of the torque is proportional to the angle θ

τ = - k θ

where k > 0 is the torque constant of the wire. The above equation is essentially a torsional equivalent to Hooke's law. The negative sign is due to restoring force.

As there are no other forces acting on the string, and from our studies of rotational motion, we know that our rotational system is (note that we are neglecting the small frictional damping force)

I α = τ = - k θ

where I is the moment of inertia in the system, and α is angular acceleration. The above equation.

Applications
1.The working of " Torsion pendulum clocks "( shortly torsion clocks or pendulum clocks), is based on torsional oscillation. 2.The freely decaying oscillation of Torsion pendulum in medium(like polymers),helps to determine their characteristic properties. 3.New researches, promising the determination of frictional forces between solid surfaces and flowing liquid environments using forced torsion pendulums.