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The Third Law
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Newton's third law also requires the conservation of momentum, 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 has pushed 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 up 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 on (almost) frictionless ice 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 skater's 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.
Energy
The quantity called energy ties together all branches of physics. In the field of mechanics, energy must be provided to do work; work is defined as the product of force and the distance an object moves in the direction of the force. When a force is exerted on an object but the force does not cause the object to move, no work is done. Energy and work are both measured in the same units-joules or foot-pounds, for example.
If work is done lifting an object to a greater height, energy has been stored in the form of gravitational potential energy. Many other forms of energy exist: electrical and magnetic potential energy; kinetic energy; energy stored in stretched springs, compressed gases, or molecular bonds; thermal energy; and mass itself. In all transformations from one kind of energy to another, the total energy is conserved. For instance, if work is done on a rubber ball to raise it, its gravitational potential energy is increased. If the ball is then dropped, the gravitational potential energy is transformed to kinetic energy. When the ball hits the ground, it becomes distorted and there is friction between the molecules of the ball material. This friction is transformed into heat, or thermal energy.
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