Mechanics (Unit 02) - Study Guide
Learn kinematics, Newton's laws, and rotational motion exam traps live.
Syllabus Core Concepts
- • Newton's 1st Law (Inertia): Every object continues in its state of rest or uniform motion in a straight line unless compelled to change that state by forces impressed upon it.
- • Law of Conservation of Angular Momentum: If the net external torque acting on a system is zero, the total angular momentum (L = Iω) of the system remains constant.
Marking Secrets & Traps
📘 Resource Book Summary: Mechanics
Core Definitions:
- • Velocity: The rate of change of displacement of an object along a specific direction.
- • Relative Velocity: The velocity of an object relative to a specific frame of reference.
- • Acceleration: The rate of change of velocity with respect to time.
Equations:
- • v = u + at
- • s = ((u + v) / 2)t
- • s = ut + ½at²
- • v² = u² + 2as (u: initial velocity, v: final velocity, a: acceleration, s: displacement, t: time)
- • Relative Velocity: v_A,B = v_A,E + v_E,B (where E is Earth)
Key Graphs:
- • Displacement - Time Graph: The gradient represents velocity.
- • Velocity - Time Graph: The gradient represents acceleration, and the area between the curve and the time axis represents displacement.
⚠️ Exam Trap Notes:
Equations of motion can only be applied to objects moving under constant acceleration. If acceleration varies, graphical methods or calculus must be used.
Core Definitions:
- • Momentum: The product of an object's mass and its velocity (p = mv).
- • Impulse: The product of the average force and the time interval during which it acts. It is equal to the change in momentum.
- • Friction: The force resisting the relative motion or tendency of motion of two surfaces in contact.
Equations:
- • Newton's Second Law: F = ma
- • Impulse: I = F × t = mv - mu
- • Law of Friction: F = μR (F: limiting/dynamic friction, μ: coefficient of friction, R: normal reaction)
Key Points:
- • Principle of Conservation of Linear Momentum: In the absence of an external unbalanced force, the total momentum of a system remains constant.
- • Limiting Friction: The maximum static friction force when an object is just on the verge of sliding.
⚠️ Exam Trap Notes:
In F = ma, F must be the resultant force acting on the object. Applying just a single individual force instead of the resultant is a common error.
Core Definitions:
- • Work: The product of the displacement and the component of the force in the direction of the displacement.
- • Power: The rate at which work is done or energy is transferred.
Equations:
- • Work Done: W = Fs cos(θ)
- • Kinetic Energy: K.E = ½mv²
- • Gravitational Potential Energy: P.E = mgh
- • Elastic Potential Energy: W = ½kx²
- • Power: P = W/t = Fv
⚠️ Exam Trap Notes:
W = Fs can only be applied when the force is constant. For variable forces (e.g., stretching a spring), the work done must be calculated using the area under the force-displacement graph (e.g., ½Fx).
Core Definitions:
- • Angular Velocity (ω): The rate of change of angular displacement with time (ω = Δθ / Δt).
- • Moment of Inertia (I): The measure of an object's resistance to changes in its rotation (I = Σmr²).
Equations:
- • Linear & Angular relations: v = rω, a_t = rα
- • Centripetal Acceleration: a_c = v²/r = rω²
- • Angular Momentum (L): L = Iω
⚠️ Exam Trap Notes:
If the net external torque is zero, angular momentum is conserved (Iω = constant). When a spinning ice skater pulls their arms in, I decreases, causing angular velocity (ω) to increase.
Core Definitions:
- • Density (ρ): Mass per unit volume (ρ = m/V).
- • Upthrust: The net upward force exerted by a fluid on any object immersed in it.
Equations:
- • Hydrostatic Pressure: P = hρg
- • Equation of Continuity: A₁v₁ = A₂v₂
- • Bernoulli's Equation: P + ½ρv² + hρg = constant
⚠️ Exam Trap Notes:
Bernoulli's equation can only be applied to steady, streamline flow of an incompressible, non-viscous fluid.
| Substance | Density (kg m⁻³) | Relative Density |
|---|---|---|
| Water | 1.0 × 10³ (1000) | 1.00 |
| Mercury | 13.6 × 10³ (13600) | 13.6 |
| Sea Water | 1.03 × 10³ (1030) | 1.03 |
⛸️ Angular Momentum Virtual Simulator
Observe the change in rotation velocity as the skater folds and extends arms.
🎯 Equations of Motion Sign Convention Tool
Practice the exam-standard sign substitution for vertical motion.