Question

Show that K.E can be expressed can be expressed a sum of K.E of motion of center of mass and K.E of motion about center of mass.?​

Answer 1

☆Concept:

》in the translatory motion, each and every particles on the rigid body will doing a pure translation motion.

》And each particle will have same same translatory parameter ,ie, distance covered,velocity ,acceleration.

》so all particle will have same velocity, or the velocity of center of mass will be same as the velocity of all particles.

☆Solution:

》$\sf{\green{ KE = \dfrac{1}{2}mv^{2}}}$

☆$\ V_{cm} = V$

》$\sf{ KE = \dfrac{1}{2}m_{total}(V_{cm})^{2}}$

☆centre of mass is the point where whole mass is concentrated,

so total mass = mass of centre of mass

》$\bf{ KE = \dfrac{1}{2}m_{cm}(V_{cm})^{2}}$

☆so we can say that in pure translation motion, kinetic energy of center of mass will be the kinetic energy of whole system

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