Mechanics — B.Sc Physics
Newton's Laws of Motion
First Law (Law of Inertia)
A body continues in its state of rest or uniform motion unless acted upon by an external force.
Inertia = Resistance to change in state of motion
Mass is measure of inertia.
Second Law
F = ma
Net force = mass × acceleration
• F in Newtons (N)
• m in kilograms (kg)
• a in m/s²
Impulse: J = F×t = Δp (change in momentum)
Third Law
Every action has equal and opposite reaction.
F₁₂ = -F₂₁
Work, Energy and Power
Work
W = F·d·cosθ
• θ = angle between force and displacement
• Work done against gravity: W = mgh
• Work = Area under F-d graph
Kinetic Energy
KE = ½mv²
Potential Energy (Gravitational)
PE = mgh
Work-Energy Theorem
Work done = Change in KE
W = ½mv² - ½mu²
Conservation of Mechanical Energy
KE + PE = constant (in absence of friction)
½mv² + mgh = constant
Power
P = W/t = F·v
Unit: Watts (W) = Joules/second
Circular Motion
Angular velocity: ω = dθ/dt (rad/s)
Linear velocity: v = rω
Centripetal acceleration: a = v²/r = rω²
Centripetal force: F = mv²/r (directed toward center)
Time period: T = 2πr/v = 2π/ω
Frequency: n = 1/T
Gravitation
Newton's Law of Gravitation:
F = Gm₁m₂/r²
G = 6.67 × 10⁻¹¹ N·m²/kg²
Acceleration due to gravity:
g = GM/R² = 9.8 m/s²
Variation of g:
• With height h: g' = g(1 - 2h/R)
• With depth d: g' = g(1 - d/R)
• At poles g is maximum, at equator minimum
Escape velocity:
vₑ = √(2gR) = 11.2 km/s
Orbital velocity:
v₀ = √(gR) = 7.9 km/s
Important Formulas — Quick Reference
``
v = u + at
s = ut + ½at²
v² = u² + 2as
s = (u+v)t/2
Momentum p = mv
Impulse J = Ft = Δp
Work W = Fs·cosθ
KE = ½mv²
PE = mgh
F_centripetal = mv²/r
F_gravity = Gm₁m₂/r²
g = 9.8 m/s²
``
PYQ
Q: A ball is thrown vertically upward with velocity 20 m/s. Find max height and time of flight.
Solution: v² = u² - 2gh → 0 = 400 - 2(10)h → h = 20m; T = 2u/g = 4s
Q: State and prove work-energy theorem.
Q: Derive expression for escape velocity.