Laws of Motion – JEE Mains Physics

1. Understanding Force

A force is any interaction that causes a change in the motion of an object or its state of rest. It is a vector quantity and measured in newtons (N).

2. Newton’s Three Laws of Motion

First Law (Law of Inertia): An object remains in its state of rest or uniform motion unless acted upon by an external force.
Second Law:The acceleration of an object is directly proportional to the net force acting on it, given by F = ma, where m is inertial mass.
Third Law: For every action, there is an equal and opposite reaction.

3. Frequently Encountered Forces

Normal Force: Acts perpendicular to the surface in contact.
Weight: Force due to gravity; given by W = mg.
Tension: Force in a string, always directed away from the body.

4. Pulley and Connected Mass Systems

Ideal pulleys and strings are assumed massless unless stated otherwise. Let's analyze a few scenarios:

(i) Vertical Pulley System (Unequal Masses)

If masses m₁ > m₂:
Acceleration: a = ((m₁ – m₂) / (m₁ + m₂)) * g
Tension: T = (2m₁m₂ / (m₁ + m₂)) * g

(ii) One Mass on a Smooth Horizontal Surface

Acceleration: a = (m₁g) / (m₁ + m₂)
Tension: T = (m₁m₂g) / (m₁ + m₂)

(iii) Horizontal Surface with Friction

Acceleration: a = ((m₁ – μm₂) / (m₁ + m₂)) * g
Tension: T = (m₁m₂(1 + μ) / (m₁ + m₂)) * g

(iv) System with Connecting Block M

a = ((m₁ – m₂) / (m₁ + m₂ + M)) * g T₁ = ((2m₂ + M) / (m₁ + m₂ + M)) * m₁g T₂ = ((2m₁ + M) / (m₁ + m₂ + M)) * m₂g

(v) Inclined Plane (Smooth)

Acceleration: a = ((m₁ – m₂ sinθ) / (m₁ + m₂)) * g
Tension: T = (m₁m₂(1 + sinθ) / (m₁ + m₂)) * g

(vi) Two Inclined Planes with Angles θ₁ and θ₂

Acceleration: a = (m₁ sinθ₁ – m₂ sinθ₂) * g / (m₁ + m₂)
Tension: T = (m₁m₂ / (m₁ + m₂)) * (sinθ₁ – sinθ₂) * g

5. Solving Motion Problems – Step-by-Step

Identify forces and accelerations involved.
Draw Free Body Diagrams (FBDs).
Resolve forces along and perpendicular to motion.
Apply Newton’s laws: F = ma and a = 0 where applicable.
Use constraint relations if necessary.
Solve the resulting system of equations.

6. Pseudo Force in Non-Inertial Frames

In accelerating frames, an additional force must be introduced for Newton’s laws to apply. For linear acceleration a, the pseudo force is -ma. For rotating frames, the centrifugal force mω²r acts outward.

7. Conical Pendulum

A conical pendulum consists of a bob revolving in a horizontal circle, with its string tracing a cone. The tension and angle depend on centripetal force requirements.

8. Apparent Weight in an Elevator

At rest/constant speed: Apparent weight = mg
Accelerating upward: m(g + a)
Accelerating downward: m(g – a)
Free fall: Apparent weight = 0
Downward acceleration > g: The body lifts off the floor.

9. Frictional Forces

Friction arises from intermolecular forces between contacting surfaces. It opposes motion and can be static or kinetic.

10. Types of Friction

Static Friction: Self-adjusting, ≤ μₛN
Limiting Friction: Maximum static friction, fₘₐₓ = μₛN
Kinetic Friction: Constant friction while sliding, fₖ = μₖN

Since μₖ < μₛ, rolling an object requires less force than sliding it.

Angle of Repose

The smallest angle of incline at which an object starts sliding. Given by: μ = tanα

If θ < tan⁻¹μ: No motion
If θ = tan⁻¹μ: Body just begins to slide
If θ > tan⁻¹μ: Motion begins with acceleration