A large wooden turntable in the shape of a flat uniform disk has a radius of 2.05 m and a total mass of 130 kg. The turntable is initially rotating at 3.40 rad/s about a vertical axis through its center. Suddenly, a 72.5-kg parachutist makes a soft landing on the turntable at a point near the outer edge.
(a) Find the angular speed of the turntable after the
parachutist lands. (Assume that you can treat the parachutist as a
particle.)
rad/s
(b) Compute the kinetic energy of the system before and after the
parachutist lands.
KEbefore | = J |
KEafter | = J |
I1 = ½Mt*R² = 0.5 x 130 x 2.052= 273.1625 kg∙m²
I2 = I1+Mp*R² = 273.1625+ 72.5*2.05² = 577.84 kg∙m²
w2 = [I1/I2]*w1 = [273.162/577.84]*3 = 1.63 rad/sec
K before = 1/2*I*ω^2 = 1/2*273.16*3.4^2 = 1578J
K after = 1/2*I*ω^2 = 1/2*577.84*1.63^2 = 768J
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