Laws of Motion — Revision Notes

⚡ 30-Second Revision

Newton's 1st Law (Inertia): — $Sigma vec{F} = 0 implies vec{v} = \text{constant}$.
Newton's 2nd Law: — $vec{F}_{\text{net}} = \frac{dvec{p}}{dt}$. For constant mass, $vec{F}_{\text{net}} = mvec{a}$.
Newton's 3rd Law: — $vec{F}_{AB} = -vec{F}_{BA}$ (Action-reaction pairs on different bodies).
Momentum: — $vec{p} = mvec{v}$.
Impulse: — $vec{J} = vec{F}_{\text{avg}}Delta t = Deltavec{p}$.
Static Friction: — $f_s le mu_s N$.
Kinetic Friction: — $f_k = mu_k N$.
Apparent Weight in Lift: — $N = m(g pm a)$ (+$a$ for upward accel., -$a$ for downward accel.).
Conservation of Momentum: — For isolated system, $Sigma vec{p}_{\text{initial}} = Sigma vec{p}_{\text{final}}$.

2-Minute Revision

The Laws of Motion are foundational to physics, explaining how forces influence an object's movement. Newton's First Law, or the Law of Inertia, states that an object maintains its state of rest or uniform velocity unless acted upon by a net external force.

This highlights that inertia, quantified by mass, is the resistance to changes in motion. Newton's Second Law, $vec{F}_{\text{net}} = mvec{a}$ (for constant mass), is the quantitative relationship, showing that net force causes acceleration proportional to the force and inversely proportional to mass.

It also defines force as the rate of change of momentum ($vec{F}_{\text{net}} = dvec{p}/dt$). Impulse, defined as the change in momentum ($Deltavec{p}$), is also $F_{\text{avg}}Delta t$. Newton's Third Law states that forces always occur in equal and opposite pairs acting on *different* objects, preventing them from cancelling out.

Key applications include analyzing friction (static and kinetic), tension in strings, normal forces (especially apparent weight in accelerating lifts), and solving problems with connected bodies or inclined planes.

Always start with a clear Free-Body Diagram and apply $Sigma F = ma$ for each object along relevant axes.

5-Minute Revision

To master Laws of Motion for NEET, focus on the core principles and their applications. Newton's First Law establishes inertia – an object's resistance to changing its state of motion. Remember, mass is the quantitative measure of inertia.

Newton's Second Law, $vec{F}_{\text{net}} = mvec{a}$, is your primary tool. It states that the net force acting on an object determines its acceleration. Crucially, force is also the rate of change of momentum ($vec{F}_{\text{net}} = dvec{p}/dt$).

This leads to the impulse-momentum theorem: $vec{J} = vec{F}_{\text{avg}}Delta t = Deltavec{p}$, vital for collision problems. Newton's Third Law, 'action-reaction,' emphasizes that forces come in pairs acting on *different* objects, meaning they don't cancel each other out.

For example, when you push a wall, the wall pushes back on you.

Problem-Solving Strategy:

1
Free-Body Diagrams (FBDs): — Always draw an FBD for *each* object in the system. Include all external forces acting *on* that object (gravity, normal force, tension, friction, applied force). Do not include forces exerted *by* the object.
2
Coordinate System: — Choose a convenient coordinate system, often aligning one axis with the direction of acceleration.
3
Resolve Forces: — Break down forces (like weight on an inclined plane) into components along your chosen axes.
4
Apply $Sigma F = ma$: — Write separate equations for each axis for each object. For example, $Sigma F_x = ma_x$ and $Sigma F_y = ma_y$.
5
Solve: — Use algebraic methods to solve the system of equations for unknowns like acceleration, tension, or normal force.

Key Applications:

Friction: — Static friction ($f_s le mu_s N$) prevents motion, while kinetic friction ($f_k = mu_k N$) opposes existing motion. Remember $mu_s ge mu_k$.
Connected Bodies/Pulleys: — Objects connected by ideal strings have the same acceleration. Tension is uniform along a massless string.
Apparent Weight: — In an accelerating lift, your apparent weight (normal force) changes. $N = m(g+a)$ for upward acceleration, $N = m(g-a)$ for downward acceleration.
Conservation of Momentum: — In the absence of external forces, the total momentum of a system remains constant. This is powerful for analyzing collisions and explosions.

Practice is paramount. Focus on understanding the 'why' behind each step in problem-solving, not just memorizing formulas.

Prelims Revision Notes

1
Inertia: — Property of matter to resist change in its state of motion. Directly proportional to mass.
2
Newton's First Law: — If $vec{F}_{\text{net}} = 0$, then $vec{a} = 0$. Object at rest stays at rest; object in motion stays in uniform motion. Defines inertial frames of reference.
3
Newton's Second Law: — $vec{F}_{\text{net}} = \frac{dvec{p}}{dt}$. For constant mass, $vec{F}_{\text{net}} = mvec{a}$. Force is a vector, direction of $vec{F}_{\text{net}}$ is same as $vec{a}$. SI unit of force is Newton (N), $1,\text{N} = 1,\text{kg}cdot\text{m/s}^2$.
4
Linear Momentum ($vec{p}$): — $vec{p} = mvec{v}$. Vector quantity. SI unit: kg·m/s.
5
Impulse ($vec{J}$): — $vec{J} = vec{F}_{\text{avg}}Delta t = Deltavec{p} = vec{p}_f - vec{p}_i$. Vector quantity. SI unit: N·s or kg·m/s. Impulse-momentum theorem.
6
Newton's Third Law: — For every action, there is an equal and opposite reaction. Forces act on *different* bodies. They do not cancel out. Examples: walking, rocket propulsion.
7
Conservation of Linear Momentum: — In an isolated system (no external forces), total linear momentum is conserved: $Sigma vec{p}_{\text{initial}} = Sigma vec{p}_{\text{final}}$.
8
Friction: — Force opposing relative motion.

* **Static Friction ($f_s$):** $f_s le mu_s N$. Acts when surfaces are at rest. Self-adjusting up to a maximum value. * **Kinetic Friction ($f_k$):** $f_k = mu_k N$. Acts when surfaces are sliding. Generally constant. $mu_s ge mu_k$.

1
Normal Force ($N$): — Perpendicular force exerted by a surface on an object in contact.
2
Tension ($T$): — Force transmitted through a string, rope, cable, or wire when pulled tight.
3
Apparent Weight in Lifts:

* At rest or constant velocity: $N = mg$. * Accelerating upwards: $N = m(g+a)$. * Accelerating downwards: $N = m(g-a)$. * Free fall ($a=g$ downwards): $N = 0$ (weightlessness).

1
Free-Body Diagrams (FBDs): — Essential for problem-solving. Isolate object, draw all external forces acting *on* it. Resolve forces into components along chosen axes (usually parallel/perpendicular to motion).
2
Connected Bodies/Pulleys: — Apply $Sigma F = ma$ to each body. If connected by ideal string, accelerations are equal, tension is uniform.

Vyyuha Quick Recall

For Motion, Always Think Inertia, Force, And Reaction.

First Law: Inertia (rest/uniform motion unless force).
Motion: Force = Mass x Acceleration ($F=ma$).
Third Law: Reaction (equal and opposite forces on different bodies).