Mechanics and Kinematics
What the exam tests
Kinematics in one and two dimensions, Newton's laws, friction, inclined planes, circular motion, work–energy and momentum. Numerical problems usually need a clear choice of axes and a free-body sketch, even when the sketch is not collected.
Core rules
- Constant acceleration: v=u+at, s=ut+½at², v²=u²+2as, s=(u+v)t/2.
- Projectile motion: horizontal velocity is constant; vertical motion has a=−g. Time of flight to the same height is 2u sinθ/g; range is u² sin2θ/g.
- Newton's second law: ΣF=ma along each chosen axis. On a frictionless incline, a=g sinθ.
- Static friction satisfies f≤μ_sN; kinetic friction is f=μ_kN and opposes relative motion.
- Conservation of mechanical energy applies when only gravity and springs do work; momentum is conserved when the external impulse is negligible.
- Uniform circular motion: a_c=v²/r toward the centre; centripetal force is a net force, not an extra one.
Worked example
A ball is launched from level ground at 20 m/s at 30° above the horizontal. Take g=9.8 m/s². u_x=20 cos30°≈17.3 m/s, u_y=20 sin30°=10 m/s. Time of flight T=2u_y/g=20/9.8≈2.04 s. Range R=u_xT≈17.3×2.04≈35.3 m. Maximum height H=u_y²/(2g)=100/19.6≈5.1 m.
Traps
- Mixing sign conventions within one problem, especially for g.
- Setting v=0 at the top and using it as the total time of flight.
- Drawing friction in the direction of motion.
- Adding an extra centripetal force to a free-body diagram.
- Using total velocity instead of its component in an energy equation.