Laws of Motion formulas for JEE Main & Advanced

20 formula entries for Laws of Motion, in the order the chapter builds them. Each shows the formula, when to use it and the first trap to avoid.

Newton's Second Law

{\vec{F}}_{net} = \frac{d \vec{p}}{d t} = m \vec{a}

When to use. Use to relate net force to acceleration for any object with constant mass.

Trap. Forgetting that ${\vec{F}}_{net}$ is the vector sum of all forces, not a single force.

Newton's Third Law

{\vec{F}}_{12} = - {\vec{F}}_{21}

When to use. Use to identify pairs of forces in interactions (e.g., normal force, tension, friction).

Trap. Thinking action-reaction forces cancel each other — they don't because they act on different objects.

Linear Momentum

\vec{p} = m \vec{v}

When to use. Use to analyze collisions, explosions, and impulse problems.

Trap. Forgetting that momentum is a vector — direction matters in collisions.

Impulse

\vec{J} = \int \vec{F} d t = Δ \vec{p}

When to use. Use when force acts over a short time (e.g., hitting a ball, catching an object).

Trap. Using average force when force is not constant — integrate or use area under F-t graph.

Normal Force

N = m g \cos θ

(on incline) or

N = m g + m a

(in accelerating lift)

When to use. Use in free-body diagrams for objects on surfaces or in contact.

Trap. Assuming normal force always equals weight — it doesn't on inclines or in accelerating frames.

Tension

T

(varies with acceleration in connected systems)

When to use. Use in problems with strings, pulleys, and connected bodies.

Trap. Assuming tension is the same on both sides of a pulley if the pulley has mass or friction.

Friction (Static and Kinetic)

f_{s} \leq μ_{s} N

f_{k} = μ_{k} N

When to use. Use whenever surfaces are in contact and relative motion is possible.

Trap. Using $f_{s} = μ_{s} N$ when the object is not at the verge of slipping — it's an inequality.

Centripetal Force

F_{c} = \frac{m v^{2}}{r} = m ω^{2} r

When to use. Use for objects in uniform circular motion (e.g., banked curves, vertical loops).

Trap. Thinking centripetal force is a separate force — it's the net radial force from tension, gravity, etc.

Pseudo Force (Inertial Force)

{\vec{F}}_{p s e u d o} = - m {\vec{a}}_{f r a m e}

When to use. Use when solving problems from an accelerating frame (e.g., a lift, a car turning).

Trap. Applying pseudo force in an inertial frame — it's only for accelerating reference frames.

Solving Connected Systems (Atwood Machine)

a = \frac{(m_{1} - m_{2}) g}{m_{1} + m_{2}}

(for simple Atwood)

When to use. Use for problems with two or more objects connected by strings over pulleys.

Trap. Assuming acceleration is g for one block — it's less due to inertia of the other block.

Lami's Theorem

\frac{F_{1}}{\sin α} = \frac{F_{2}}{\sin β} = \frac{F_{3}}{\sin γ}

When to use. Use for problems with three forces acting at a point (e.g., hanging mass, tension in wires).

Trap. Using it when forces are not concurrent or not in equilibrium.

Constraint Relations (String Length Constant)

a_{1} + a_{2} = 0

(for two blocks on same string over pulley) or more complex relations.

When to use. Use in problems with multiple pulleys or moving pulleys.

Trap. Forgetting sign conventions — assign positive direction for each block consistently.

Banking of Roads (Optimal Speed)

v_{0} = \sqrt{r g \tan θ}

When to use. Use for problems on banked curves without friction or with friction.

Trap. Using this formula when friction is present — then use $v^{2} / r = g (\tan θ + μ) / (1 - μ \tan θ)$ .

Vertical Circular Motion (Minimum Speed at Top)

v_{top, min} = \sqrt{g r}

When to use. Use $\sqrt{g r}$ at the top for a mass on a string (or inside a track), where tension/normal force cannot be negative; for a rod/tube/bead on a wire, $v_{t o p} \geq 0$ and $v_{b o t t o m} \geq 2 \sqrt{g r}$ .

Trap. Assuming speed is constant — it's not; use energy conservation.

Impulse-Momentum Theorem

\vec{J} = {\vec{p}}_{f} - {\vec{p}}_{i}

When to use. Use when force acts over a short time or when final/initial velocities are known.

Trap. Forgetting sign of velocity (direction) when calculating change.

Conservation of Linear Momentum

\sum {\vec{p}}_{i} = \sum {\vec{p}}_{f}

When to use. Use for collisions, explosions, and recoil problems.

Trap. Applying it when external forces are present (e.g., friction, gravity) — only if net external force is zero.

Equilibrium of a Particle

\sum F_{x} = 0

\sum F_{y} = 0

When to use. Use for stationary objects or objects moving with constant velocity.

Trap. Forgetting to include all forces (e.g., tension, normal, weight).

Spring Force (Hooke's Law)

F = - k x

When to use. Use for problems involving springs, oscillations, or elastic forces.

Trap. Forgetting the negative sign (direction opposite to displacement).

Pulley Systems (Movable Pulley)

a_{load} = \frac{1}{2} a_{effort}

(for single movable pulley)

When to use. Use for problems with block and tackle or complex pulley arrangements.

Trap. For a movable pulley the string tension $T$ is the same on both sides only if the pulley is ideal (massless, frictionless); the pulley is then supported by $2 T$ . A massive pulley gives different tensions.

Friction on Inclined Plane

f_{s} \leq μ_{s} m g \cos θ

f_{k} = μ_{k} m g \cos θ

When to use. Use for any object on an inclined plane with friction.

Trap. Using $m g$ as normal force — it's $m g \cos θ$ .

Values to remember

$μ_{s} > μ_{k}$ Friction (Static and Kinetic)
$g = 9.8 {m/s}^{2}$ Banking of Roads (Optimal Speed)

Read the full chapter: Laws of Motion for JEE, with what JEE asks and the common traps.