Space, Time and Motion: Mechanics, Kinematics, Forces, Momentum, Energy, Circular Motion and Gravitation
Space, time and motion is the mechanics core of IB Physics HL. Questions test your ability to choose a kinematic model, apply Newton’s laws to single and linked bodies, use momentum and energy conservation, analyse circular motion, and link gravitational field strength to orbits. Many HL items combine two models, so define the system and positive direction before substituting numbers.
Core rules
- The suvat equations apply only when acceleration is constant; choose one positive direction and keep it.
- Newton’s second law is F_net = ma. On an incline the normal force is mg cosθ, not mg.
- Impulse FΔt = Δp; momentum is conserved when the net external force on the system is zero.
- Work W = Fs cosθ; the work–energy theorem gives ΔE_k = W_net. Mechanical energy is conserved only without non-conservative work.
- Circular motion: a = v²/r = ω²r, directed to the centre. Centripetal force is the resultant, not an extra force.
- Gravitation: g = GM/r², orbital speed v = √(GM/r), and T² = 4π²r³/(GM).
Worked example
A satellite orbits 600 km above Earth. Take Earth’s radius as 6.37 × 10⁶ m and GM = 3.99 × 10¹⁴ m³ s⁻². The orbital radius is r = 6.97 × 10⁶ m. Then v = √(GM/r) = √(5.73 × 10⁷) = 7.57 × 10³ m s⁻¹. The period is T = 2πr/v = 5.79 × 10³ s, about 96 minutes. The reasoning uses the gravitational force as the centripetal resultant, not a separate force.
Traps
Do not add a separate centripetal force to a free-body diagram. In inelastic collisions momentum is conserved but kinetic energy is not. Do not assume g is constant over large height changes. Check that sinθ and cosθ are assigned to the correct component on inclines.