How to Calculate Kinetic Energy Relative to Center of Mass?

[lebprince]

Homework Statement

Consider a system consisting of three particles:
m1 = 4 kg, 1 = < 10, -4, 15 > m/s
m2 = 6 kg, 2 = < -14, 6, -4 > m/s
m3 = 3 kg, 3 = < -21, 39, 19 > m/s

(a) What is the total momentum of this system?
(b) What is the velocity of the center of mass of this system?
(c) What is the translational kinetic energy of this system?
(d) What is the kinetic energy of this system relative to the center of mass?
(e) What is the total kinetic energy of this system?

The Attempt at a Solution

i was able to solve parts a , b, c and i know that part e is the addition of part c + part d , i need help on part d. Thanks

 

[tiny-tim]

Consider a system consisting of three particles:
m1 = 4 kg, 1 = < 10, -4, 15 > m/s
m2 = 6 kg, 2 = < -14, 6, -4 > m/s
m3 = 3 kg, 3 = < -21, 39, 19 > m/s
…
(d) What is the kinetic energy of this system relative to the center of mass?

Hi lebprince!

Velocities are vectors, so they obey vector addition (and subtraction!).

If the velocities of the masses and the c.o.m. are A B C and V,

then find the vectors VA VB and VC …

that gives you velocities of the masses relative to to the c.o.m. …

from which you can get the KE relative to to the c.o.m.