Question

Estimate the magnitudes of these quantities?

Sit down with your feet on the ground on a chair that rotates. Lift one of your legs such that it is unbent (straightened out). Using the other leg, begin to rotate yourself by pushing on the ground. Stop using your leg to push the ground but allow the chair to rotate. From the origin where you began, sketch the angle, angular velocity, and angular acceleration of your leg as a function of time in the form of three separate graphs. Estimate the magnitudes of these quantities.

Answer 1

Well, I tried this but take it as an attempt because I am not sure I correctly interpreted the question....

Explanation:

I immagined that the action of your leg gives you an angular velocity (initial) but this is reduced gradually because of, say, friction immediatelly after you start rotating. Your angular velocity `omega` should decrease, let us say, steadily because of this constant negative angular acceleration `alpha`.

In the graphs I supposed a very heavy action of friction so that the chair almost stops after a turn!

I tried with my rotating chair and it took `7.8sec` to stop completing (more or less) 3 revolutions (it is quite old).
Let us use (assuming constant `alpha`):
`theta=((omega_i+omega_f)/2)t`
`3*2pi=((omega_i+0)/2)7.8`
rearranging:
`omega_i=4.83"rad"/"sec"`

The angular acceleration will be:
`alpha=(omega_f^2-omega_i^2)/(2theta)=(0-4.83^2)/(2*3*2pi)=-0.62"rad"/s^2`

Well take it as an attempt...