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isolated system, conservation of momentum, momenta, internal forces, axis of rotation

Newton’s third law of motion states that an object experiences a force because it is interacting with some other object. The force that object 1 exerts on object 2 must be of the same magnitude but in the opposite direction as the force that object 2 exerts on object 1. If, for example, a large adult gently shoves away a child on a skating rink, in addition to the force the adult imparts on the child, the child imparts an equal but oppositely directed force on the adult. Because the mass of the adult is larger, however, the acceleration of the adult will be smaller.

Newton’s third law also requires the conservation of momentum, or the product of mass and velocity. For an isolated system, with no external forces acting on it, the momentum must remain constant. In the example of the adult and child on the skating rink, their initial velocities are zero, and thus the initial momentum of the system is zero. During the interaction, internal forces are at work between adult and child, but net external forces equal zero. Therefore, the momentum of the system must remain zero. After the adult pushes the child away, the product of the large mass and small velocity of the adult must equal the product of the small mass and large velocity of the child. The momenta are equal in magnitude but opposite in direction, thus adding to zero.

Another conserved quantity of great importance is angular (rotational) momentum. The angular momentum of a rotating object depends on its speed of rotation, its mass, and the distance of the mass from the axis. When a skater standing on a friction-free point spins faster and faster, angular momentum is conserved despite the increasing speed. At the start of the spin, the skater’s arms are outstretched. Part of the mass is therefore at a large radius. As the skater’s arms are lowered, thus decreasing their distance from the axis of rotation, the rotational speed must increase in order to maintain constant angular momentum.

Article key phrases:

isolated system, conservation of momentum, momenta, internal forces, axis of rotation, rotational speed, skating rink, skater, magnitude, acceleration, Newton, interaction, opposite, opposite direction, constant, mass, direction, arms, distance, force, example, child, addition, law, start, adult, work, order

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