Question

Two ice-skaters, whose masses are 45 kg and 75 kg, hold hands and rotate about a vertical axis that passes between them, making one revolution in 3 s. Their centers of mass are separated by 1.7 m, and their center of mass is stationary. Model each skater as a point particle.

(a) Find the angular momentum of the system about it's center of mass.
___________________ J·s_________J.s
(b) Find the total kinetic energy of the system.

_______J

Answer 1

a) We locate the center of mass from the 45 kg mass:

$x_{cm} = 1.7(75)/(45+75)= 1.0625 m$

The moment of inertia is:

$I = mr_1^2+mr_2^2 = 45(1.0625)^2+75(0.6375)^2= 81.2813 kgm^2$

the angular moment is given by:

$L = I\omega =I\frac{2\pi}{T}=\frac{81.2813*2\pi}{3}=170.24 Js$

b)The total energy is given by:

$K = \frac{L^2}{2I}= \frac{170.24^2}{2(81.2813)}= 178.28J$

The angular momentum of the systen is given by: