Teaching Physics with the Physics Suite Edward F. Redish

Linear and rotational momenta and energies

In the figure below are shown snapshots of four situations in which a set of 4 point masses are moving in various configurations. The masses are all identical and each has a mass m. Their speeds are all identical and have the value v, and each mass is a distance R from the place where the dotted lines cross (the system origin). Use the coordinate directions shown on the right but for each system take the origin to be at the indicated crossing of the dotted lines.

The arrows indicate the direction of motion of the masses at the instant the snapshot was taken. Where a thin ring is shown, the masses are attached to a light (nearly massless) plastic hoop.

Calclulate the values of the total linear momentum, angular momentum, and total energy of motion in the four cases. (Be sure to include an indicator of the direction where appropriate.) Rank their magnitudes from largest to smallest. For the case of the energy of motion, discuss how much of the energy you would assign to rotational kinetic energy and why.

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