ANALYSIS:

The experiment is

about moment of inertia. In

the experiment we are to

determine the mass of

moment of inertia of a disk

and a ring and to compare

the moment of inertia of

solid disk rotated at two

different axes: at the center

and along its diameter. The

moment of inertia of an

object about a given axis

describes how difficult it is to change its angular motion about that axis. Therefore,

it encompasses not just how much mass the object has overall, but how far each bit

of mass is from the axis. The further out the object's mass is, the more rotational

inertia the object has, and the more rotational force (torque, the force multiplied by

its distance from the axis of rotation) is required to change its rotation rate.

For example, consider two wheels suspended so they can turn freely, a

large bicycle wheel and a small baby buggy wheel. Suppose they have the same

weight, which means they have equal mass. It requires more effort (torque) to spin

(accelerate) the bicycle wheel to a given angular velocity than the baby buggy

wheel. This is because the rim of the bicycle wheel is further from its axis than the

rim of the baby buggy wheel. Even though they have the same amount of mass,

most of the mass of the bicycle wheel is located farther from the axis than the mass

in the baby buggy wheel, so it must move faster for a given rotation rate. So the

bicycle wheel has a larger moment of inertia than the baby buggy wheel.

The moment of inertia of an object can change if its shape changes. Figure skaters

who begin a spin with arms outstretched provide a striking example. By pulling in

their arms, they reduce their moment of inertia, causing them to spin faster by the

conservation of angular momentum.

The moment of inertia has two forms, a scalar form, I, (used when the axis

of rotation is specified) and a more general tensor form that does not require the

axis of rotation to be specified. The scalar moment of inertia, I, (often called

simply the "moment of inertia") allows a succinct analysis of many simple

problems in rotational dynamics, such as objects rolling down inclines and the

behavior of pulleys. For instance, while a block of any shape will slide down a

frictionless decline at the same rate, rolling objects may descend at different rates,

depending on their moments of inertia. A hoop will descend more slowly than a

solid disk of equal mass and radius because more of the hoop's mass is located far

from the axis of rotation. However, for (more complicated) problems in which the

axis of rotation can change, the scalar treatment is inadequate, and the tensor

treatment must be used (although shortcuts are possible in special situations).

Examples requiring such a treatment include gyroscopes, tops, and even satellites,

all objects whose alignment can change. The moment of inertia is also called

the mass moment of inertia (especially by mechanical engineers) to avoid

confusion with the second moment of area, which is sometimes called the area

moment of inertia (especially by structural engineers).

In the first part of the experiment we are ask to determine the moment of

inertia of disk and ring

rotated about the center.

We set up the equipments

according to the manual.

In order to determine the

moment of inertia of disk

and ring we add a small

mass to overcome kinetic

friction. After overcoming

kinetic friction we performed the procedures and get the acceleration. Using the

equation in the manual we get the average of the three trials. Referring to table 1;

the percent difference between the average computed value of the moment of

inertia and the actual value of moment of inertia of disk and ring is 6.81%. The

percentage error is quite big; this is due to some errors that we might commit

during the experiment.

In the second part of

the experiment we are ask to

determine the moment of

inertia of disk rotated about

the center. We set up the

equipments according to the

manual. In order to determine

the moment of inertia of disk

we add a small mass to

overcome kinetic friction just

like in the first part. After overcoming kinetic friction we performed the procedures

and get the acceleration. Using the equation in the manual we get the average of

the three trials. Referring to table 2; the percent difference between the average

computed value of the moment of inertia of the disk and the actual value of

moment of inertia of disk is 6.54%. The percentage error is quite big; this is due to

some errors that we might commit during the experiment just like in the first part.

In the third part of the experiment we are ask to determine the moment of

inertia of ring. We computed the moment of inertia of ring using the equation in

the manual. Referring to table 3; the percent difference between the value of the

moment of inertia of the ring and the actual value of moment of inertia of ring is

0.0006%. Therefore the value that we computed is very close to the actual value of

the moment of inertia of ring.

In the fourth part

of the experiment we are

ask to determine the

moment of inertia of disk

rotated about the

diameter. We set up the

equipments according to

the manual. In order to determine the moment of inertia of disk we add a small

mass to overcome kinetic friction just like in the first part. After overcoming

kinetic friction we performed the procedures and get the acceleration. Using the

equation in the manual we get the average of the three trials. Referring to table 4;

the percent difference between the average computed value of the moment of

inertia of the disk and the actual value of moment of inertia of disk is 9.36%. The

percentage error is quite big; this is due to some errors that we might commit

during the experiment just like in the first part.

TABLE 4. Determination of Moment of Inertia of Disk (rotated about the diameter)

Mass of disk, MDISK = 1401.1 grams

Radius of disk, RDISK = 11.4 cm

Actual value of moment of inertia of disk

IDISK = ¼ MDISK R2

IDISK = 45521.74 g-cm2

Friction mass = 5 grams radius, r = 2.96 cm

TRIAL (mass of pan + mass added), m Acceleration, a

Experimental value of moment

of inertia, I = m(g – a)r 2

a

1 5 grams 1.5 cm/s2 28577.42 gcm2

2 10 grams 1.5 cm/s2 57154.84 gcm2

3 15 grams 12 cm/s2 64266.34 gcm2

average 49992.87 gcm2

% difference 9.36 %