# Moment of Inertia of swivel chair

1. Sep 3, 2011

### Afphan

Question:
While sitting in a swivel chair, you push against the floor withyour heel to make the chair spin. The 7.1 frictional force is appliedat a point 45 from the chair'srotation axis, in the direction that causes the greatest angularacceleration.
If that angular acceleration is 1.5 , what is thetotal moment of inertia about the axis of you and the chair?

I solved it like :

Its actually torque that is the tendency to rotate an object is equal to the perpendicular force at a distance --- T= F * d (Newton-meter is SI unit) -- i found out the torque and then there z relation between Torque and angular acceleration and Moment of Inertia similar to Newton's second law F=MA only the difference is that its not for linear processes but rotational processes (So here Torque is the force , Mass is Moment of Inertia and Linear acceleration is converted to angular acceleration) so T = I . a (T = moment of a force , I = Moment of Inertia , a = angular acceleration ) so it would be like I = T / a = ****(7.1 N * 0.45 m) / 1.5 radpersec^2 **** I = (Ans) Kg/m^2 >>>>>>>>> do check it !

Then for my personal experience i did following experiment :-

Observation = While sitting on a swivel chair , i pushed against the floor with my heel to make the chair of 8 kg spin and i used stop watch to calculate its angular velocity , after 1 second and 20 centiseconds (approx) as calculated it maintained constant 1 rev/sec velocity for further 5 seconds . The frictional force was applied at a 55 cm from the chair's rotation axis. I weigh 65 kg.

Find moment of inertia about my axis and chair ----Answer = kg * m^2

Solution :-

1. Since constant angular velocity is calculated through experiment, we can apply formula to measure constant angular acceleration (radi/sec)

*Angular acceleration = omega (angular velocity) / time
a (angular acceleration) = 6.92 / 1.2 = 5.76 radi / sec^2

2. To calculate frictional force applied , Newton's of law of inertia can be used :-
F = m * a

F (tangential) = m * a (tangential)

//a (tan) = r * a (angular.a)//

<F (tan) = m * r a (angular.a)>

(where F = frictional force , m = mass , r = moment arm and a = angular mass)

Lets suppose i need to add both masses = 73 Kg

F = 73 * 0.55 * 5.76 = 231.264 N

3. Calculate Torque = T = F x r = 127.20 Nm

4. In order to calculate Moment of inertia , use its relation with torque and angular acceleration = T = I * a (where T= torque, I= moment of inertia , a = angular acceleration)

I = T / a = 127.2 / 5.76

I = 22.0825 Kg.m^2

Note :-

Just check my observations out and if i'm wrong , how actually to find out moment of inertia or an irregular shaped body like swivel chair