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Running Head: THE TORSION OF A PENDULUM

The Torsion of a Pendulum

Students Name

Institutional Affiliation

1

THE TORSION OF A PENDULUM

2

Objectives

To compare the experimentally determined moment of inertia of several bodies with

corresponding theoretical value

Theory

In general, the motion of a rigid body is combination of translational and rotational motion. The

description of the rotational portion of the motion involves both rotational kinematics and

rotational dynamic.

Consider a rigid body rotating with angular speed about an axis that is fixed in a particular

reference frame. A particle of mass m at a distance r from the axis of rotation moves in a circle

of radius r with angular speed about this axis and has linear speed v = r. Its kinetic energy is

1

1

K = 𝑚𝑣 2 − 𝑚𝑟 2 2

2

2

If the body is a rigid, is the same for all the particles in the body but r is different from each

particle. Hence, the total kinetic energy of the rotating of body is

1

1

𝐾 = ( 𝑚1 𝑟12 + 𝑚2 𝑟22 . . ) 2 = (𝑚1 𝑟12 )2

2

2

The term 𝑚1 𝑟12 is denoted by the symbol I and I called moment of inertia or the rotational

inertia of the body with respect to the particular axis of rotation.

For a body that is not composed of that discrete point masses but is a continuous distribution of

matter, the equation

𝐼 = 𝑚1 𝑟12

THE TORSION OF A PENDULUM

3

Is replaced by 𝐼 = ʃ𝑟 2 𝑑𝑚

Consider a long uniform wire, rigidly clamped at its upper end and supporting at its lower end a

circular disk whose moment of inertia about an axis through the wire is I . If the disk is rotated

through some angles, a restoring torque, Ʈ, is a setup in the wire tending to bring the disk back to

its equilibrium position. When the disk is released the torque gives the disk an angular

acceleration

Ʈ = 𝐼𝛼

The restoring torque set up in the wire when its lower end is twisted th...

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