Teacher License – Physics Complete Review Guide 2026–2027

4. Newton's second law: \(\sum F = ma\), with acceleration along the net force. First law: a body at rest or at constant velocity has zero net force. Third law: two forces equal in size and opposite in direction acting on two different bodies (6.6.5, 3).
5. Kinetic friction \(f_k = \mu_k N\) and maximum static friction \(f_s \le \mu_s N\). On an incline at angle \(\theta\), the weight component along the plane is \(mg\sin\theta\) and perpendicular to it is \(mg\cos\theta\) (6.6.5, 3).
6. Momentum \(p = mv\) and impulse \(F\Delta t = \Delta p\). Total momentum is conserved when the net external force is zero. In an elastic collision kinetic energy is also conserved, in an inelastic one it is not, and in a perfectly inelastic one the bodies stick together at a common speed \(v = (m_1v_1 + m_2v_2)/(m_1 + m_2)\) (6.6.5, 4).
7. Uniform circular motion: constant speed but changing direction, centripetal acceleration \(a_c = v^2/r\) toward the centre, centripetal force \(F_c = mv^2/r\), and \(v = \omega r = 2\pi r/T\) (6.6.5, 5).
8. Torque \(\tau = rF\sin\theta\) (unit N·m), where \(r\sin\theta\) is the perpendicular lever arm. Equilibrium of a rigid body needs both \(\sum F = 0\) and \(\sum \tau = 0\), and a net torque produces angular acceleration \(\sum\tau = I\alpha\) (6.6.5, 6).
9. Universal gravitation: \(F = Gm_1m_2/r^2\) with \(G = 6.67\times10^{-11}\ \text{N}\cdot\text{m}^2/\text{kg}^2\). The force is inversely proportional to the square of the distance between centres, and surface gravity is \(g = GM/R^2\) (6.6.5, 7).
10. Work \(W = Fd\cos\theta\), kinetic energy \(KE = \tfrac{1}{2}mv^2\), gravitational potential energy \(PE = mgh\), power \(P = W/t\). Work-energy theorem: \(W_{net} = \Delta KE\) (6.6.5, 8).
11. Mechanical energy \(KE + PE\) is conserved when only conservative forces act (gravity, springs). Friction removes some of it as heat, yet total energy stays conserved. Spring energy is \(\tfrac{1}{2}kx^2\) (6.6.5, 8).
12. Relative motion: \(\vec v_{A/B} = \vec v_A - \vec v_B\), and measured velocity changes with the reference frame. A boat crossing a river at 4 m/s perpendicular to a 3 m/s current moves at 5 m/s relative to the bank (3-4-5 triangle) (6.6.5, 9).
13. Archimedes' principle: the buoyant force on a fully or partly submerged body equals the weight of fluid displaced, \(F_b = \rho_f V_{sub} g\). For a cylinder submerged to height \(h\), \(F_b = \pi r^2 \rho g h\). A body floats if its density is less than the fluid's, and at rest while floating \(F_b = W\) (6.6.6, 1).
14. Continuity for an incompressible fluid: \(A_1 v_1 = A_2 v_2\) (volume flow rate is constant), so speed rises where the cross-section narrows. Bernoulli along a streamline: \(P + \tfrac{1}{2}\rho v^2 + \rho g h = \text{constant}\), so pressure drops where speed rises at the same height (6.6.6, 2 and 3).
15. Pascal's principle: pressure applied to a confined fluid is transmitted undiminished to every point, so a hydraulic press obeys \(F_1/A_1 = F_2/A_2\). Pressure is \(P = F/A\) in pascals (\(\text{Pa} = \text{N/m}^2\)), and at depth \(h\) it is \(P = P_0 + \rho g h\) (6.6.6, 4 and 5).
16. Viscosity is a fluid's resistance to flow (internal friction), in Pa·s. Liquid viscosity falls as temperature rises while gas viscosity rises. Cohesion is attraction between molecules of the same substance, adhesion between molecules of different substances (6.6.6, 5 and 6).

Common mistakes in this chapter

• ✕ Mass versus weight: mass is the same everywhere (kg), while weight \(W = mg\) is a force (N) that changes with \(g\). An orbiting object is not weightless; it is in continuous free fall.
• ✕ Distance, speed, displacement and velocity: distance and speed are scalars, displacement and velocity are vectors. A body that returns to its start has zero displacement but non-zero distance.
• ✕ At the top of a projectile's path only the vertical velocity component is zero; the acceleration is still \(g\) downward and the horizontal component is unchanged (air resistance neglected).
• ✕ The two forces of an action-reaction pair act on different bodies, so they never cancel each other. A book's weight and the normal force from the table are not an action-reaction pair.
• ✕ Inelastic collisions: momentum is always conserved in an isolated system, but kinetic energy decreases. Choosing \"kinetic energy is conserved\" for a collision where the bodies stick together is a common error.
• ✕ Centripetal force is not an extra force to draw in a free-body diagram; it is the net force toward the centre (tension, gravity, friction). \"Centrifugal force\" is only spoken of in a non-inertial reference frame.
• ✕ Doubling the speed multiplies kinetic energy by four (\(KE \propto v^2\)), not two, and doubling the distance between two masses cuts the gravitational force to one quarter, not one half.
• ✕ Buoyant force depends on the submerged volume and the fluid's density, not on depth or the object's weight. In Pascal's principle the force is multiplied but not the work: the large piston moves a shorter distance.