A torsional pendulum is made from a plumb bob having of mass m = 0.1 kg suspende

Question

A torsional pendulum is made from a plumb bob having of mass m = 0.1 kg suspended from a thin, fibrous chord having a torsional constant ? = 2.4 ? 10-4 N?m/rad and negligible mass. The plumb bob can be thought of consisting of a cylinder measuring 2.5 cm in diameter and having a height of 1.5 cm, connected to a cone with a base diameter of 2.5 cm and height of 3.5 cm as shown above. What is the period of this torsional pendulum? Hint: We can find the moment of inertia of the plumb bob by finding the moments of inertia for the cylinder and cone and adding those together. The moment of inertia for a cone rotating through its central axis is 23 10 cone cone I m r = , while the moment of inertia for a cylinder rotating through its central axis is 21 2 cylinder cylinder I m r = . Another hint: We will need to determine the masses of the cylindrical and conical parts separately. We can find these masses by finding the density of the whole plumb bob and then multiplying this by the volume of the cylinder and the volume of the cone. Don’t know the formula for the volume of a cone? 2 1 3cone V r h p = . What? You don’t know the formula for the volume of a cylinder, either? Look it up! 9-3

Explanation / Answer

Ans)mass of the plumb bob m=0.1kg

Torsional constant k=2.4x10-4 N-m/rad

Diameter of the cylinder d=2.5cm

Radius of the cylinder r=d/2=2.5/2=1.25cm

Therefore r=0.0125m

Height of the cylinder h=1.5cm=0.015m

Volume of the cylinder V=?r2h

V=(3.14)x(0.0125)2x(0.015)

=7.36x10-6 V

Volumeof cone V=(1/3)?r2h

=(1/3)x3.14x(0.0125)2x0.015

2.45x10-6 V

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