Physics

Problem

Two point masses form a rigid system in the

xy

-plane. Mass

m_1 = 1.0\,\text{kg}

is located at

(0.40\,\text{m},\,0)

and mass

m_2 = 2.0\,\text{kg}

is located at

(-0.20\,\text{m},\,0)

. At a particular instant their velocities are

\mathbf{v}_1 = (1.0\,\hat{i}+1.6\,\hat{j})\,\text{m/s}

and

\mathbf{v}_2 = (1.0\,\hat{i}-0.8\,\hat{j})\,\text{m/s}

. (i) Compute the total kinetic energy of the system directly from these velocities. (ii) Compute the sum of the translational kinetic energy of the center of mass and the rotational kinetic energy about the center of mass, and show that this sum equals the result from part (i). Report the common numerical value.

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