Force and motion explains how forces change the motion of objects. You will learn about the concept of inertia, the relationship between force and acceleration, action–reaction pairs, and real-life applications like walking, driving, rocket propulsion and frictional effects. The chapter links everyday observations to Newton’s laws and teaches how to model forces using free-body diagrams and equations (mainly F = m·a).

1. Inertia — Newton's First Law

Inertia is the tendency of an object to resist change in its state of motion. Mass is a quantitative measure of inertia — objects with larger mass have greater inertia. Example: a heavy table resists being pushed; if a car suddenly stops, passengers lurch forward due to their inertia.

2. Newton's Second Law — quantitative link

The second law gives the relationship F = m·a. This is a vector equation — acceleration occurs in the direction of net force. For constant mass, a = F/m. Always consider net (resultant) force: if multiple forces act, first sum them vectorially, then apply F_net = m·a.

3. Newton's Third Law — action and reaction

Action and reaction forces act on different bodies and are equal in magnitude and opposite in direction. Important to remember: they do not cancel because they act on different objects.

4. Friction — types and behavior

Friction opposes relative motion between surfaces. Two main types:

• Static friction: prevents motion up to a maximum value (f_s ≤ μ_s·N).
• Kinetic friction: opposes motion when sliding occurs (f_k = μ_k·N typically less than μ_s·N).

N is the normal reaction. Coefficients μ_s, μ_k depend on surfaces.

5. Momentum & impulse

Momentum is mass×velocity. Impulse from a force over time equals change in momentum (J = F·Δt = Δp). Shorter impact times (like hitting with a hammer vs cushioned) produce larger forces for the same change in momentum—hence helmets and padding reduce impact forces by increasing Δt.

1. Example 1 — Using F = m·a
   A 2 kg block is pulled by a 10 N horizontal force on a frictionless surface. Find acceleration.
   Solution steps:

   1. Draw free-body diagram: horizontal force = 10 N, no friction.
   2. Apply F_net = m·a → 10 = 2 · a.
   3. So a = 10 / 2 = 5 m/s².
2. Example 2 — Action–reaction (two bodies)
   A boy of mass 40 kg stands on a skateboard and pushes a wall. The boy experiences a force of 20 N backward from the wall. What is the boy's acceleration?
   Solution:

   1. Action: boy pushes wall (on wall). Reaction: wall pushes boy with 20 N opposite direction.
   2. Apply F = m·a → a = F/m = 20 / 40 = 0.5 m/s² (in direction of reaction force).
3. Example 3 — Friction problem
   A 10 kg crate rests on horizontal floor. Coefficient of static friction μ_s = 0.4. Find maximum horizontal force that can be applied without moving the crate. (g = 9.8 m/s²)
   Solution:

   1. Normal reaction N = mg = 10 × 9.8 = 98 N.
   2. Maximum static friction = μ_s × N = 0.4 × 98 = 39.2 N.
   3. Therefore maximum applied horizontal force without motion ≈ 39.2 N.
4. Example 4 — Momentum & impulse
   A 0.2 kg ball moving at 15 m/s is brought to rest by a constant force in 0.1 s. Find the force magnitude.
   Solution:

   1. Initial momentum = m·v = 0.2 × 15 = 3 kg·m/s. Final momentum = 0.
   2. Change in momentum Δp = −3 kg·m/s. Impulse J = Δp = F·Δt → F = Δp / Δt = −3 / 0.1 = −30 N.
   3. Magnitude of force = 30 N (opposite to motion).
5. Example 5 — Inclined simple frictionless (conceptual)
   A block of mass 5 kg slides down a frictionless plane making 30° with horizontal. What is acceleration down the plane? (g = 9.8 m/s²)
   Solution:

   1. Component of gravitational force along plane = mg sinθ = 5 × 9.8 × sin30° = 49 × 0.5 = 24.5 N.
   2. Net force = 24.5 N down plane. So a = F/m = 24.5 / 5 = 4.9 m/s² down the plane.

• Action–reaction pair clarity: they act on different bodies — never cancel on same body.
• Net force vs applied force: include friction, normal reaction, weight and other forces to compute net.
• Sign convention: choose positive direction and be consistent. If acceleration is opposite chosen positive direction, its sign will be negative.
• Units: convert km/h to m/s by ×(5/18) before using F = m·a or momentum equations.
• Free-body diagrams: always draw them — they reduce mistakes and show which forces cancel or add.

1. What is inertia? Ans: Tendency of object to resist change in motion; measured by mass.
2. A 3 kg object accelerates at 2 m/s². What net force acts on it? Ans: 6 N.
3. Two skaters push off each other; one recoils faster. Why? Ans: Equal and opposite forces produce equal and opposite impulses; smaller mass ⇒ larger speed (p conserved).
4. When does static friction do work? Ans: Static friction does work only if point of contact moves relative to ground — typically zero work for rolling without slipping.
5. Why are airbags useful? Ans: They increase stopping time Δt for given Δp, reducing force (F = Δp/Δt) on occupant.

Q: Do action and reaction act on the same body?
A: No — action acts on one body and reaction on another.

Q: Is friction always a force that opposes motion?
A: Yes; static friction opposes tendency to move, kinetic opposes actual relative motion.

Q: Can acceleration be zero when multiple forces act?
A: Yes — if net force is zero (forces balance), acceleration is zero (object at rest or moving uniformly).

Remember: Inertia → Newton I; F_net = m·a → Newton II; Action–Reaction → Newton III. Momentum and impulse connect force with change in motion over time. Friction introduces resistance and depends on normal reaction and surface properties. Solve problems by drawing forces, summing them, and applying Newton’s laws consistently.