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Tension is the pulling force exerted by a rope or string, acting along its length. In an ideal massless inextensible string, tension is constant throughout and acts to accelerate both connected objects as if they were a single system.
Analyze systems with pulleys and multiple masses. Use free-body diagrams for each object separately, then apply constraints that relate their accelerations through the rope geometry.
Tension is not always equal to an object's weight. In a pulley system, the tension in a rope changes if the rope passes over a pulley with friction or if the pulley has significant mass.
From Newton's Third Law you know that contact forces come in pairs, and from your study of normal force you know how surfaces transmit pushes perpendicular to their face. Tension is the complementary contact force: strings and cables transmit *pulls* along their length. A string can only pull its two endpoints toward each other — it cannot push them apart. This is the fundamental asymmetry between strings (which only pull) and rigid rods (which can both push and pull). If you try to push with a string, it goes slack and transmits no force.
The two simplifying assumptions — massless and inextensible — define the ideal string and make tension problems tractable. A massless string has no weight of its own to support and no inertia of its own to accelerate. This means every cross-section of the string must transmit the same force: if one end pulls with tension T, the whole string pulls with tension T. You can verify this with Newton's Second Law applied to any segment of the string: net force = (mass of segment) × acceleration = 0 × a = 0, so the forces on both ends of any segment must be equal and opposite — the tension is constant throughout. An inextensible string doesn't stretch, so the speed and acceleration of both endpoints are constrained to be equal (for a straight string) or related by the geometry (for strings over pulleys).
In free-body diagrams, tension forces always point *away from* the object and *along* the string. For a ball hanging from a ceiling by a rope: draw the tension arrow pointing upward along the rope from the ball toward the ceiling. The rope is also pulling the ceiling downward — those are Newton's Third Law partners — but they act on the ceiling, not the ball, so they don't appear on the ball's free-body diagram.
Pulley problems show the power of these idealizations. Connect mass A (hanging on the left) to mass B (hanging on the right) over a frictionless, massless pulley. The string tension is the same throughout — call it T. Write Newton's Second Law for each mass separately: for A (taking down as positive), m_A·g − T = m_A·a. For B (taking up as positive), T − m_B·g = m_B·a. The constraint that the string doesn't stretch means both masses have the same magnitude of acceleration a. Now you have two equations and two unknowns (T and a). Solving: a = (m_A − m_B)g / (m_A + m_B), and T = 2m_A·m_B·g / (m_A + m_B). Notice that T is less than either weight — the rope can't be pulling A up as hard as A's full weight, or A wouldn't accelerate down.
When the idealizations break down — a rope with significant mass, a pulley with friction or rotational inertia — tension is no longer constant along the rope. A massive rope on a table must support the weight of the rope below it, so tension increases with height. A frictional pulley creates different tensions on its two sides, which is how a capstan (winch) works: a small force on one side can hold a large load on the other. These complications require the same conceptual framework — Newton's Second Law applied to each element — extended to handle the additional physics.