Lower 6 Cameroon A-Level Physics: Mechanics (Detailed Notes)
1. Introduction to Mechanics
Mechanics is the branch of physics concerned with the study of motion, forces, energy, and momentum. It forms a core part of the Lower 6 Cameroon syllabus.
Main topics include:
- Kinematics (motion in one and two dimensions)
- Dynamics (forces, Newton’s laws)
- Work, Energy, and Power
- Linear momentum and Impulse
- Gravitation
- Oscillations and circular motion
2. Kinematics
Kinematics describes motion without considering the forces causing it.
2.1 Scalars and Vectors
- Scalars: magnitude only (e.g., speed, distance, mass, energy)
- Vectors: magnitude and direction (e.g., velocity, displacement, acceleration, force)
2.2 Displacement, Velocity, and Acceleration
Displacement: s = x_final - x_initial
Velocity: v = ds/dt (instantaneous),
Average: v_avg = Δs/Δt
Acceleration: a = dv/dt (instantaneous),
Average: a_avg = Δv/Δt
2.3 Equations of Motion (Constant Acceleration)
v = u + at
s = ut + 1/2 at²
v² = u² + 2as
s = ((u+v)/2) × t
Where: u = initial velocity, v = final velocity, a = acceleration, t = time, s = displacement
2.4 Motion in Two Dimensions
Break motion into x and y components:
v_x = v cos θ, v_y = v sin θ
x = u_x t, y = u_y t - 1/2 g t²
Projectile motion: horizontal velocity constant, vertical motion under gravity.
3. Dynamics
Dynamics deals with forces and their effects on motion.
3.1 Newton’s Laws of Motion
- 1st law: An object remains at rest or moves with constant velocity unless acted upon by a resultant force.
- 2nd law: F = m × a (force equals mass times acceleration)
- 3rd law: For every action, there is an equal and opposite reaction.
3.2 Types of Forces
- Weight: W = m × g
- Normal force
- Friction: static and kinetic
- Tension in strings or cables
- Applied force
3.3 Friction
f = μ × N
where μ = coefficient of friction, N = normal reaction
3.4 Circular Motion
For uniform circular motion:
Centripetal acceleration: a_c = v² / r
Centripetal force: F_c = m × v² / r
Where r = radius, v = speed, m = mass
4. Work, Energy, and Power
4.1 Work Done
W = F × d × cos θ
Work is positive when force and displacement are in same direction; negative if opposite.
4.2 Kinetic and Potential Energy
KE = 1/2 m v²
PE = m g h
Law of conservation of energy: Total energy remains constant in an isolated system.
4.3 Power
P = W / t = F × v (if force and velocity are in same direction)
5. Linear Momentum and Impulse
5.1 Linear Momentum
p = m × v
Where p = momentum, m = mass, v = velocity
5.2 Impulse
J = F × Δt = Δp
Impulse = change in momentum. Useful in collision problems.
5.3 Conservation of Momentum
In absence of external forces, total momentum before collision = total momentum after collision.
6. Gravitation
Newton’s law of universal gravitation:
F = G × (m₁ m₂) / r²
Where G = 6.674 × 10⁻¹¹ N·m²/kg², r = distance between centers
6.1 Acceleration Due to Gravity
g = G × M / R²
Where M = mass of planet, R = radius of planet
6.2 Orbital Motion
Centripetal force = gravitational force: m v² / r = G m M / r² → v = √(G M / r)
Orbital period: T = 2π r / v
7. Oscillations (Simple Harmonic Motion)
7.1 SHM Basics
Displacement varies sinusoidally with time:
x = A cos(ω t + φ)
Velocity: v = dx/dt = -A ω sin(ω t + φ)
Acceleration: a = dv/dt = -ω² x
7.2 Period and Frequency
T = 2π / ω
f = 1 / T
7.3 Energy in SHM
Total energy: E = 1/2 k A² (constant)
KE = 1/2 m v², PE = 1/2 k x²
8. Example Problems
Example 1: A car accelerates from 0 to 20 m/s in 10 s. Find acceleration and distance traveled.
Solution: a = Δv / t = 20 / 10 = 2 m/s²
s = ut + 1/2 at² = 0 + 0.5 × 2 × 10² = 100 m
Example 2: A 2 kg mass moves in a circle of radius 0.5 m at 4 m/s. Find centripetal force.
Solution: F_c = m v² / r = 2 × 16 / 0.5 = 64 N
9. Diagram Placeholders
- Kinematics diagram: displacement, velocity, acceleration
- Projectile motion
- Free-body diagram
- SHM: mass-spring
10. Tips for Exams
- Always label diagrams with directions of forces, velocity, acceleration.
- Break vectors into components for 2D motion problems.
- Write down known quantities and unknowns before solving.
- Check units for consistency (m/s, N, J, kg).
- Derive formulas step by step if required.