Engineering Mechanics Practice Exam

When a planet moves under a central gravitational force, the torque about the center (the sun) is zero because the force points along the radius. That makes the angular momentum about the sun constant. Angular momentum for the planet is L = m r × v, and in planar motion its magnitude is L = m r v_t, with v_t the tangential component of velocity. Since dL/dt = r × F = 0 for a central force, L does not change as the planet orbits. This conservation leads to Kepler’s second law: equal areas are swept in equal times, meaning the planet adjusts its speed so that the product of its radius and its tangential speed stays the same as it moves. The other possibilities don’t stay constant in general. Linear momentum of the planet isn’t constant because gravity (an external force) acts on it. Kinetic energy isn’t constant because gravitational potential energy is exchanged with kinetic energy as the planet moves closer to or farther from the sun. Only the total mechanical energy of the planet-sun system is conserved. Speed itself isn’t constant either, since the planet speeds up when closer to the sun and slows down when farther away.