Laws of Motion and Forces — NDA Physics

Formulas (1)

• What a force is — the foundation · Definition of the newton (from Newton's second law)
  $$1\,\text{N} = 1\,\text{kg} \cdot 1\,\text{m s}^{-2}$$

Reference tables (3)

Watch out for (3)

• Force is a vector — direction matters
  → What a force is — the foundation
• Friction is a contact force; magnetism is non-contact — ALWAYS
  → Fundamental forces vs contact forces
• Gravity acts as the RESTORING force for a pendulum
  → Equilibrium and restoring forces

Formulas (5)

• First law — inertia · Condition for the first law (equilibrium of motion)
  $$\vec{F}_{\text{net}} = 0 \iff \vec{a} = 0$$
• Second law — F = ma · Newton's second law
  $$\vec{F} = \frac{d\vec{p}}{dt} = m\vec{a} \quad (\text{constant } m)$$
• Third law — action and reaction · Newton's third law (force pair)
  $$\vec{F}_{AB} = -\vec{F}_{BA}$$
• Combining forces — the parallelogram law · Magnitude of the resultant of two forces
  $$R = \sqrt{P^2 + Q^2 + 2PQ\cos\theta}$$
• Rotational inertia — moment of inertia of common bodies · Moment of inertia of common bodies (mass M, radius R)
  $$I_{\text{ring}} = MR^2, \quad I_{\text{disc}} = \tfrac{1}{2}MR^2, \quad I_{\text{sphere}} = \tfrac{2}{5}MR^2$$

Reference tables (1)

Watch out for (8)

• Constant velocity does NOT mean changing speed
  → First law — inertia
• Force is proportional to rate of change of momentum, NOT to momentum itself
  → Second law — F = ma
• Watch the units when computing F = ma
  → Second law — F = ma
• Action-reaction pairs act on DIFFERENT bodies
  → Third law — action and reaction
• Two equal forces with a resultant equal to each: θ = 120°
  → Combining forces — the parallelogram law
• Don't add force magnitudes arithmetically
  → Combining forces — the parallelogram law
• Mass is the constant of proportionality, NOT weight
  → Mass vs weight
• Same mass + radius, different I — distribution decides
  → Rotational inertia — moment of inertia of common bodies

Formulas (2)

• Linear momentum, p = mv · Linear momentum
  $$\vec{p} = m\vec{v}$$
• Impulse = change in momentum; the cushioning principle · Impulse-momentum theorem
  $$J = F\,\Delta t = \Delta p = m(v - u)$$

Watch out for (3)

• On an elastic bounce, momentum changes but speed and KE don't
  → Linear momentum, p = mv
• Cushioning increases TIME to reduce FORCE
  → Impulse = change in momentum; the cushioning principle
• Net force on the floor in a bounce includes weight
  → Impulse = change in momentum; the cushioning principle

Formulas (3)

• Conservation of linear momentum · Conservation of momentum (two bodies)
  $$m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2$$
• Force when mass is added or ejected (variable mass) · Force to maintain speed while loading mass at rate dm/dt
  $$F = v\,\frac{dm}{dt}$$
• Collisions — elastic and the equal-mass result · Equal-mass elastic head-on collision (m₂ initially at rest)
  $$v_1' = 0, \qquad v_2' = u_1$$

Watch out for (4)

• Internal forces can't move the centre of mass
  → Conservation of linear momentum
• Vertically-falling mass adds no horizontal momentum
  → Force when mass is added or ejected (variable mass)
• Equal-mass elastic collision: velocities are EXCHANGED
  → Collisions — elastic and the equal-mass result
• Use momentum (not KE) to find the unknown speed
  → Collisions — elastic and the equal-mass result

Formulas (2)

• Limiting (maximum) friction, f = μN · Limiting friction
  $$f_{\max} = \mu N$$
• Friction as the only horizontal force — stopping a block · Friction from stopping (work-energy form)
  $$f \, s = \tfrac{1}{2} m u^2 \;\Rightarrow\; f = \frac{m u^2}{2s}$$

Reference tables (1)

Watch out for (1)

• Use the correct normal force, not always mg
  → Limiting (maximum) friction, f = μN