Rotational Dynamics

The purpose of this experiment is to prove that moment of inertia is affected by mass of the object.


The theory of this experiment is as follows :
Torque is the tendency of a force to rotate an object about some axis, and it is defined by the formula :

Torque = F . r . sin theta
where
F is the force; and
r is the length of the position vector from axis of rotation to the point of application of force.

Torque is an analogy to force; forces cause acceleration while torques cause angular acceleration.

The angular acceleration is inversely proportional to moment of inertia, I.

I = m . r²
where
m is the mass of the object or small points on the object; and
r is the distance of the mass from axis of rotation.

Moment of inertia depends on the quantity of the matter and its distribution in the rigid object and also on the location of the axis of rotation.

If the net external torque acting on the system is zero, the angular momentum (L) remains constant and conservation of angular momentum can be applied, i.e.

Li = Lf

I_i . omega_i² = I_f.omega_f²

m_i . r_i² . omega_i² = m_f . r_f² . omega_f²

Tools needed :
1. A ceiling fan that has not been cleaned up for 8 months or so
2. A broom, or a mop, or anything with long stick and an end that can be used for cleaning.
3. A place to stand, be it a desk near the ceiling or stairs.


Experiment Procedures :
1. Clean and tidy up things around the experimental area. If possible, also cover them with plastic wrapper or anything.
2. Hold the broom in your hand.
3. Climb up the desk and stand carefully. Make yourself stable on the table.
4. Using the tip of the broom, try to reach the ceiling fan.
5. Wipe off the dusts attached to the ceiling; let them fall into the floor. It is better if you have already prepared a place (pail/carton box) to collect the dusts from the fan.
6. After the ceiling fan is cleaned up thoroughly, clean the dust on the floor. Also return all the things to its normal place.
7. Switch on the ceiling fan.


This experiment can be considered succesful if your ceiling fan rotates faster and produce cooler breeze than usual.
It is because :

m_i . r_i² . omega_i² = m_f . r_f² . omega_f²

Because r is the same in both condition (i.e. same ceiling fan), we can cancel out r in both sides, hence the equation becomes :

m_i . omega_i² = m_f . omega_f²

As m_f is smaller than m_i, so omega_f is bigger than omega_i.

Dusts wiped off make the ceiling fan lighter, so omega (angular acceleration) after experiment is bigger than that before experiment, as the result, the fan will rotate faster.


It is really worth to try! *lol*

anyway, posting yang
sulit-setengah-tewas-bikin-ampir-buta formattingnya ini intinya cuma : saya
udah bersihin kipas angin kamar saya.