Question

A torsion pendulum consists of an irregularly-shaped object of mass 29.0 kg suspended vertically by a wire of torson constant 1.14 Nm through its center of mass. If this pendulum oscillates through 98 cycles in 74.0 s, find the rotational inertia of the object.

Answer 1

Answer:

$I=0.0503\ kg-m^2$

Explanation:

Given that,

Mass of the object, m = 29 kg

Torsion constant of the wire, K = 1.14 N-m

Number of cycles, n = 98

Time, t = 74 s

To find,

The rotational inertia of the object.

Solution,

Relationship between the moment of inertia, time period and the torsion constant of the spring is given by :

$T=2\pi\sqrt{\dfrac{I}{K}}$

Where I is the moment of inertia

K is spring constant

Let T Is the time period of oscillation, such that,

$T=\dfrac{98}{74}=1.32\ s$

$I=\dfrac{T^2K}{4\pi ^2}$

$I=\dfrac{(1.32)^2\times 1.14}{4\pi ^2}$

$I=0.0503\ kg-m^2$

So, the rotational inertia of the object is $0.0503\ kg-m^2$.