Two point masses form a rigid system in the -plane

PHYSICS · Subjective · AP · Physics C: Mechanics · Energy and Momentum of Rotating Systems · Energy and Momentum of Rotating Systems

Problem

Two point masses form a rigid system in the xyxy-plane. Mass m1=1.0 kgm_1 = 1.0\,\text{kg} is located at (0.40 m, 0)(0.40\,\text{m},\,0) and mass m2=2.0 kgm_2 = 2.0\,\text{kg} is located at (−0.20 m, 0)(-0.20\,\text{m},\,0). At a particular instant their velocities are v1=(1.0 ı^+1.6 ȷ^) m/s\mathbf{v}_1 = (1.0\,\hat{\imath}+1.6\,\hat{\jmath})\,\text{m/s} and v2=(1.0 ı^−0.8 ȷ^) m/s\mathbf{v}_2 = (1.0\,\hat{\imath}-0.8\,\hat{\jmath})\,\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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