Physics
Vectors and Equilibrium
4,341 words, 10 sections
This chapter is syllabus unit Physics 1, Vectors and Equilibrium, and it carries 131 distinct questions across 56 official papers between 2001 and 2026, examined by Balochistan, DUHS, Federal, KMU, NUMS and UHS, with a mean item difficulty of 1.82 and 719 active questions behind it in the practice bank. Physics is worth 36 marks of the 180-mark paper, and this unit supplies a large share of its arithmetic. The load is uneven: vector addition and resolution accounts for 64 of those questions, scalar and vector products for 48, and conditions of equilibrium for 18. A student who can resolve any force into rectangular components, take both products by components, and apply the two conditions of equilibrium will answer almost every numerical the paper sets from this chapter.
A scalar is a quantity fully described by a magnitude and a unit. Mass, time, temperature, distance, speed, work, energy and pressure are scalars. A vector needs a magnitude, a unit and a direction before the statement is complete. Displacement, velocity, acceleration, force, weight, momentum, impulse and torque are vectors. The test is not whether the quantity sounds physical or whether it is about motion; it is whether a direction can be attached to it without changing the meaning. Mass is a scalar, while weight is the same quantity multiplied by gravity and is a vector because gravity acts in a definite direction. Distance is a scalar and displacement is a vector; speed is a scalar and velocity is a vector.
The direction requirement explains several results that look surprising at first. A body can have a large speed and a zero velocity if it returns to its starting point, because the straight-line displacement is then zero. A quantity can carry a word that suggests direction and still be a scalar: electromotive force is a scalar, and so is electric flux, because flux is the scalar product of the field and the vector area. In three-dimensional space a vector needs three independent components to fix it, so a vector in space has three dimensions.
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