K_{tot} = K_{trans} + K_{rel}

Consider a system consisting of three particles:

m_{1} = 2 kg, v_{1} < 10, -5, 12 > m/s

m_{2 }= 9 kg, v_{2 }<- 14, 3, -3>m/s

m_{3 }= 2 kg, v_{3 }<- 23, 37, 20 > m/s

What is the kinetic energy of this system relative to the center of mass?

K_{rel} = J

One way to calculate Krel is to calculate the velocity of each particle relative to the center of mass, by subtracting the center-of-mass velocity from the particle's actual velocity to get the particle's velocity relative to the center of mass, then calculating the corresponding kinetic energy, then adding up the three relative kinetic energies However, there is a much simpler way to determine the specified quantity, without having to do all those calculations; think about what you know about the relationships among the various kinds of kinetic energy in a multiparticle system. (If you wish, you can check your result by doing the complicated calculation just described.)

The total kinetic energy of the system is 3530J and the translational kinetic energy of the system is J.

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