A student on a stool rotates freely at 180 rounds per minute. The student holds a 1.00 kg mass in each outstretched arm, 0.8 m from the axis of rotation. The combined moment of inertia of the student and the stool is 6.00 kgm2 which remains constant. How far should the student pull his arms inward so that the rotation becomes 4.00 Hz?
physics !! - Graham, Friday, August 30, 2013 at 11:46pm
180 rounds per minute = 3.00 Hz
Angular momentum of each mass is:
L = (m r^2)ω
Mass and Angular momentum are conserved, so:
r0^2 ω0 = r1^2 ω1
r1 = r0 √(ω0/ω1)
r1 = 0.800 √(3.00/4.00)
r1 ≈ 6.93m
physics !! - kent, Saturday, August 31, 2013 at 12:52pm
how u calculate i calculate get 0.693m .
can u explain to me ??how u did this ~ why the 3Hz /4Hz?
physics !! - Graham, Sunday, September 1, 2013 at 2:05am
My apology for the typo. I must have miskeyed during calculation, but I should have realised that seven meter was a bit of an arm stretch.
So yes, r1 ≈ 0.693m
Because angular momentum and mass are conserved, the angular velocity is inversely proportional to the square of the radius. Thus to increase the frequency from 3.00Hz to 4.00Hz requires decreasing the radius from 0.800m to 0.693m.
(r1/r0) = √(ω0/ω1)
(6.93m/0.800m) = √(3.00Hz/4.00Hz)