Mechanics and Motion
Mechanics and Motion
This domain covers kinematics, Newton's laws, vectors, projectile and circular motion, and gravitation. The exam tests whether you can choose a coordinate system, separate motion into components, and identify the forces acting on a body before applying F = ma.
Core rules and concepts
- Average velocity is displacement over time; instantaneous velocity is the limit as the time interval approaches zero. Acceleration is the rate of change of velocity.
- For constant acceleration, use v = v0 + at, Δx = v0t + ½at², and v² = v0² + 2aΔx.
- Newton's first law defines inertial frames; the second law is a vector equation; the third law pairs act on different bodies and never cancel on the same body.
- Projectile motion: horizontal velocity is constant (neglecting air resistance), vertical acceleration is g downward.
- Uniform circular motion requires a net centripetal force directed toward the center; the force is provided by tension, gravity, friction, or a normal force-not an extra centripetal force added to the diagram.
Worked example
A 2.0 kg block on a frictionless surface is pulled by a 10 N force at 30° above horizontal. Horizontal acceleration: Fx = 10 cos30° = 8.66 N; a = Fx/m = 4.3 m/s². The vertical component affects the normal force but not horizontal acceleration on a frictionless surface.
Traps that cost marks
Using speed and velocity interchangeably; forgetting that g is downward; adding centripetal force as a separate force; and mixing up action-reaction pairs, which act on different objects. In projectile problems, never assume vertical velocity is zero at launch unless stated.