KFUPM Tahsili Complete Review Guide 2026–2027

4. Momentum p=mv is a vector; impulse FavgΔt=Δp requires signed velocities. A 0.1 kg ball reversing from +8 to −6 m/s receives impulse −1.4 N·s, not −0.2 N·s. Total momentum is conserved when external impulse is negligible. Elastic collisions also conserve kinetic energy; equal masses exchange velocities in a one-dimensional elastic collision. Objects that stick share one final velocity: a 3 kg cart at 4 m/s sticking to a stationary 1 kg cart moves at 3 m/s. A uniform rod has its center of mass at its midpoint by symmetry.
5. For objects orbiting the same planet in circular orbits, T² is proportional to r³. Measure r from the planet’s centre. Increasing r by a factor of four increases the orbital period by a factor of eight.
6. A lever in equilibrium has zero net torque about its pivot. For perpendicular forces of 9 N at 0.40 m and 12 N at 0.30 m on opposite sides, the clockwise and counterclockwise torque magnitudes are both 3.6 N·m if both forces point downward.
7. Temperature differences have the same numerical size in K and °C, but absolute temperature is T(K)=T(°C)+273.15; ideal-gas average translational kinetic energy is proportional to K. Without phase change, Q=mcΔT. In an insulated mixture, heat lost equals heat gained, including any container specified. During melting at fixed pressure, Q=mLf changes phase rather than temperature. Conduction rate is kAΔT/d, convection moves fluid, and radiation crosses vacuum. Example: 0.25 kg of water with c=4200 J/(kg·K) warmed by 8 K absorbs 8400 J.
8. From longer to shorter wavelengths, the spectrum runs from radio waves through microwaves, infrared, visible light, ultraviolet and X-rays to gamma rays. In vacuum a shorter wavelength corresponds to a higher frequency.

Common mistakes in this chapter

• ✕ Include rest time in average speed; subtract opposite displacements, not path lengths.
• ✕ Use net force and net work. Third-law partners belong to different objects; absence of friction alone does not guarantee constant mechanical energy.
• ✕ A rebound reverses the velocity sign. Sticking conserves momentum in an isolated collision, but does not conserve kinetic energy.
• ✕ Convert cm² by 10⁻⁴ and cm³ by 10⁻⁶. Use kelvin for absolute-temperature ratios and Q=mL on a phase-change plateau.
• ✕ Use the same positive rotation direction for all torques. A force acting through the axis has zero torque.