Mechanics: Motion, Forces, Energy, and Momentum
Domain 2: Mechanics: Motion, Forces, Energy, and Momentum
This domain tests translational motion, Newton's laws, circular motion, work and energy, impulse and momentum, and conservation laws. Items often require choosing the right principle rather than brute-force algebra.
Core rules
- Kinematics for constant acceleration: v = v0 + at, Δx = v0t + ½at², and v² = v0² + 2aΔx. Choose a sign convention and keep it.
- Newton's second law: ΣF = ma. On an incline, the normal force is mg cos θ, not mg. Static friction can range up to μsN; kinetic friction is μkN and opposes sliding.
- Work = Fd cos θ; work–energy theorem: Wnet = ΔK. Mechanical energy is conserved only when nonconservative work is zero.
- Impulse J = FΔt = Δp. Momentum is conserved in collisions when external impulse is negligible; kinetic energy is conserved only in elastic collisions.
- Uniform circular motion has centripetal acceleration v²/r toward the center; the force is not a new outward force.
Worked example
A 2.0 kg block starts from rest and slides 5.0 m down a frictionless 30° incline. The vertical drop is h = 5.0 sin 30° = 2.5 m. Conservation of energy gives ½mv² = mgh, so v = √(2gh) = √(2 × 9.8 × 2.5) = √49 ≈ 7.0 m/s. Mass cancels. If friction were present, subtract friction work μkNd from mgh before solving.
Traps that cost marks
- Saying momentum is conserved in every collision but assuming kinetic energy is too.
- Using mg for normal force on an incline.
- Confusing centripetal force with an extra outward force.
- Mixing up distance and displacement, or speed and velocity.
- Forgetting that the work done by a force perpendicular to motion is zero.