JEE Laws of Motion: Newton’s Laws, Force, Momentum and Constraints Notes by Physics Wallah

Most mistakes in Laws of Motion come before any formula is used. A force is drawn in the wrong direction, an action-reaction pair is treated as if it acts on one body, or a weighing machine reading is confused with weight. Once the free-body diagram is right, the calculation is usually short. JEE questions reflect this: they test whether you can identify the forces, choose the correct axes and apply Newton’s second law without slipping on signs.

Physics Wallah’s Laws of Motion notes follow that order. They begin with force and momentum, move through Newton’s three laws and impulse, and then cover free-body diagrams, common forces, inclined planes, pulley constraints and accelerated frames. Draw the diagram for every problem you practise, state which body you are analysing and check each result against the condition it assumes, such as an ideal string or a frictionless surface.

Force and Momentum

Force is an interaction that can change a body’s velocity by changing its speed, direction or both. Its effect depends on the body’s inertia, which is related to mass.

Momentum is the product of mass and velocity:

p = mv (a vector)

• SI unit: kg m/s

• Dimensional formula: [M L T⁻¹]

The change in momentum is:

Δp = p(f) − p(i)

Momentum is a vector, so its direction must be considered while solving problems.

Newton’s Laws of Motion

Newton’s First Law: Law of Inertia

A body remains at rest or continues moving with constant velocity unless a non-zero net external force acts on it.

Inertia is the tendency of a body to resist changes in its state of motion. Greater mass means greater inertia.

If F(net) = 0, then a = 0

Newton’s Second Law

The net external force equals the rate of change of momentum:

F(net) = dp/dt

For a body of constant mass:

F(net) = ma

The SI unit of force is the newton (N), where 1 N = 1 kg m/s².

Newton’s Third Law

For every action, there is an equal and opposite reaction. These forces act on different bodies, so they do not cancel each other in the free-body diagram of a single body.

For example, when you push a wall, the wall exerts an equal and opposite force on you.

Impulse and Momentum

Impulse measures the effect of a force acting over a time interval. It equals the change in momentum.

J = Δp

For a constant force:

J = F Δt

The area under a force-time graph gives the impulse.

For the same change in momentum, a longer time of impact gives a smaller average force. This is why a cricketer moves their hands backwards while catching a fast ball.

Free-Body Diagrams and Common Forces

A free-body diagram (FBD) shows a body separately, with all the external forces acting on it. Draw the FBD before applying Newton’s laws.

Weight

Weight is the gravitational force on a body:

W = mg

Near Earth’s surface, it acts vertically downward.

Normal Reaction

The normal reaction is the contact force exerted by a surface. It acts perpendicular to the contact surface and pushes the body away from it.

For a body on a smooth horizontal surface with no other vertical acceleration: N = mg

The normal reaction is not always equal to weight. Its value depends on the forces and acceleration involved.

Tension

Tension is the pulling force transmitted through a stretched string or rope. An ideal string is massless and inextensible, and it cannot push.

For an ideal string over a frictionless, massless pulley: T₁ = T₂

A slack string has zero tension.

Spring Force

Hooke’s law gives the restoring force of an ideal spring:

F(s) = −kx

Here k is the spring constant and x is the displacement from the natural length. The negative sign shows that the force acts opposite to the displacement.

For a vertical spring in equilibrium:

• kx = mg

• x = mg / k

Equilibrium and Motion on an Inclined Plane

A body is in equilibrium when its acceleration is zero. It may be at rest or moving with constant velocity.

ΣFₓ = 0 and ΣFᵧ = 0

For a body on a smooth incline at angle θ, resolve its weight into two components:

• Along the incline: mg sin θ

• Perpendicular to the incline: mg cos θ

If the body slides down a smooth incline:

• a = g sin θ

• N = mg cos θ

When drawing an FBD on an incline, choose one axis parallel to the surface and the other perpendicular to it. This simplifies the force equations.

Constraints in Strings and Pulleys

Constraints relate the motion of connected bodies. For an inextensible string, the total length stays constant.

In a simple fixed-pulley system, the connected bodies have equal acceleration magnitudes:

|a₁| = |a₂|

Their directions depend on how the string is arranged.

For a movable pulley supported by two segments of an ideal string, if the free ends have signed velocities v(A) and v(B), the pulley velocity is:

v(P) = (v(A) + v(B)) / 2

Use a consistent sign convention for every pulley constraint. For bodies that stay in contact, the relative acceleration along the common normal must satisfy the contact condition.

Pseudo Force and Accelerated Frames

A frame accelerating relative to an inertial frame is a non-inertial frame. To apply Newton’s laws in it, introduce a pseudo force:

F(pseudo) = −m a(frame)

It acts opposite to the acceleration of the frame.

For a person in an elevator:

• At rest or at constant velocity: N = mg

• Accelerating upward with acceleration a: N = m (g + a)

• Accelerating downward with acceleration a: N = m (g − a)

• In free fall: N = 0

A weighing machine measures the normal reaction, which may differ from the gravitational weight mg.

For a pendulum in a car accelerating horizontally with acceleration a, the angle θ between the string and the vertical satisfies:

tan θ = a / g

Important Points to Remember

• Momentum is p = mv, while force is the rate of change of momentum.

• F = ma applies directly to constant-mass systems.

• Action and reaction act on different bodies.

• Impulse equals the change in momentum.

• Normal reaction acts perpendicular to the contact surface.

• An ideal string has equal tension throughout when it passes over an ideal pulley.

• Resolve forces along convenient axes on inclined planes.

• Apply string constraints using a consistent sign convention.

• Pseudo force acts opposite to the acceleration of a non-inertial frame.

Laws of Motion rewards a fixed routine: choose the body, draw its free-body diagram, pick convenient axes and then apply Newton’s second law along each one. Revise the conditions behind the standard results, such as equal tension for an ideal string and N = mg only when there is no vertical acceleration. Then practise problems on pulleys, inclined planes, impulse and elevators until each step becomes automatic. PW’s Laws of Motion notes support your JEE revision by keeping these formulas and their conditions together in one place.

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