Physics Laboratory 5
Rotational Moment of Inertia
1. Objective
To enhance the understanding of rotation and rotational moment of inertia for
both of particle (point mass) and rigid body. In addition, students must be able to find
rotational moment of inertia and compare it with the theoretical value.
2. Theory and Principle
If the line of the net force passes through the center of mass of the object, it
will cause only translation. However, if the line of the net force hits on the object
along other directions, there will induce the moment of force or torque which leads to
rotation.
In this experiment, we will focus on only the rotation around fixed axis.
Theoretically, in case of very small object (particle or point mass), the induced
torque follows the following relation:
τ = Fr (1)
Where τ = Torque (N.m)
r = radius of rotation (m)
From F = mat
(2)
And at = αr (3)
Substitute (2) and (3) into (1)
τ = m r
2
α (4)
Where at
= Tangential acceleration along the circumference of rotation
(perpendicular to radius of rotation)
α = angular acceleation (rad/s2
)
Figure 5.1 Circular rotation of object with mass m- 2 -
The m r2 is the value which shows the characteristic of rotation. If m r2 is high, it is
required a large amount of torque to induce rotation as well as to stop rotating object.
Therefore, m r2 is the term that informs us about the resistance of rotation or the
rotational moment of inertia.
Then
Rotational Moment of Inertia = 2
I = mr (kg.m2
)
In case of larger object or rigid body, while facing non-zero torque, the
equation of rotation should be the same as the particle. However, the rotational
moment of inertia will be the summation of m r2 of each particle.
For rigid body
Rotational Moment of Inertia = 2
i i
I = Σm r (kg.m2
)
= ∫
I r dm 2
In this experiment, from the previous equation, we can find the theoretical