Newton's Laws of Motion (NLM) and Friction - Notes for Quick Revision 📚

Newton's Laws of Motion (NLM) form the backbone of classical mechanics, describing the relationship between an object's motion and the forces acting on it. Friction, a force that opposes motion, is a key concept closely tied to these laws. Together, they are essential for understanding and solving problems in mechanics.

This article provides detailed notes on Newton's Laws of Motion (NLM) and Friction, including definitions, formulas, applications, and problem-solving techniques.

Newton's Laws of Motion (NLM)

1. First Law of Motion (Law of Inertia)

Statement: An object remains in its state of rest or uniform motion in a straight line unless acted upon by an external force.

Key Concepts:

• Inertia: The tendency of an object to resist changes in its state of motion.
• Applications: Seatbelts in vehicles, objects at rest staying stationary unless pushed.

2. Second Law of Motion

Statement: The rate of change of momentum of an object is directly proportional to the net external force applied and occurs in the direction of the force.

Formula: $$F=ma$$ Where:

• $F$: Net force ($\text{N}$).
• $m$: Mass of the object ($\text{kg}$).
• $a$: Acceleration (${\text{m/s}}^2$).

Applications: Rockets, moving vehicles, falling objects under gravity.

3. Third Law of Motion

Statement: For every action, there is an equal and opposite reaction.

Key Concepts:

• Action and reaction forces act on different bodies and are equal in magnitude but opposite in direction.
• Applications: Jet propulsion, swimming, recoil of a gun.

Key Concepts in NLM

1. Force

A physical interaction that changes or tends to change the state of motion of an object.

Unit: $\text{Newtgn (N)}$.
Types of Forces:

• Contact Forces: Friction, tension, normal force.
• Non-Contact Forces: Gravitational, electrostatic, magnetic forces.

2. Momentum

• Defined as the product of an object's mass and velocity: $$p = mv$$
• SI Unit: $\text{kg·m/s}$.

3. Impulse

• The change in momentum caused by a force acting over a time interval: $$J = F \Delta t$$
• Unit: $\text{N·s}$.

4. Free-Body Diagrams (FBDs)

• Diagrams used to represent forces acting on an object.
• Important for solving problems in mechanics.

Friction

Friction is the force that opposes the relative motion of two surfaces in contact.

Types of Friction

Static Friction ($f_s$):

• Prevents the motion of an object at rest.
• Maximum static friction: $$f_s\le {\mu }_{s}N$$ Where ${\mu }_s$: Coefficient of static friction, $N$: Normal force.

Kinetic Friction ($f_k$):

• Opposes the motion of an object sliding over a surface.
• Formula: $$f_k={\mu }_{k}N$$ Where ${\mu }_k$: Coefficient of kinetic friction.

Rolling Friction:

• Occurs when an object rolls over a surface.
• Much smaller than static or kinetic friction.

Laws of Friction

1. Friction is independent of the contact area, as long as the normal force remains constant.
2. Friction is proportional to the normal force.
3. Kinetic friction is constant and less than maximum static friction.

Key Formulas in Friction

Frictional Force:

$$f=\mu N$$

Where:

• $\mu$: Coefficient of friction.
• $N$: Normal force.

Inclined Plane:

• Net force along the incline: $$F_{\text{net}}=mg\sin \theta -f$$

Work Done Against Friction:

$$W=fd$$

Where $d$: Displacement of the object.

Applications of Friction

Driving:

Friction between tires and the road enables vehicles to accelerate, decelerate, and turn.

Braking Systems:

Relies on frictional forces to slow down vehicles.

Machines:

Lubricants are used to reduce friction and wear in mechanical systems.

Comparison of Static and Kinetic Friction

Property	Static Friction	Kinetic Friction
Occurrence	Acts when an object is at rest.	Acts when an object is in motion.
Magnitude	Varies up to a maximum value.	Constant for a given set of surfaces.
Coefficient ($\mu$)	$\mu_s > \mu_k$	$\mu_k < \mu_s$

Problem-Solving Strategies

For NLM Problems:

• Draw a free-body diagram.
• Resolve forces into components along axes.
• Apply $F=ma$ along each axis.

For Friction Problems:

• Determine the type of friction (static, kinetic, or rolling).
• Calculate normal force and use it to find the frictional force.

Examples and Applications

1. Block on a Horizontal Surface

Given a block of mass $m$ with a horizontal force $F$, find its acceleration.

• Solution: $$f_k={\mu }_{k}N,N=mg,F_{\text{net}}=F-f_k,a=\frac{F_{\text{net}}}{m}$$

2. Block on an Inclined Plane

A block of mass $m$ slides down an incline at angle $\theta$. Find the acceleration.

• Solution: $$F_{\text{net}}=mg\sin \theta -f_k,a=\frac{F_{\text{net}}}{m}$$

FAQs About NLM and Friction

What is the relationship between friction and motion?

Friction opposes relative motion between two surfaces and plays a crucial role in starting, stopping, and controlling motion.

Why is static friction greater than kinetic friction?

Static friction is greater because it involves stronger interlocking of surface irregularities, which are disrupted during motion.

What are the limitations of Newton’s Laws?

Newton’s Laws are valid only in inertial frames of reference and fail for very small particles or near the speed of light.

Can friction ever be eliminated?

Friction cannot be entirely eliminated but can be significantly reduced using lubricants or smooth surfaces.

Newton's Laws of Motion (NLM) and friction are central concepts in mechanics, providing a framework to analyze motion and the forces acting on objects. Understanding the principles of NLM and the characteristics of friction enables students to solve problems ranging from simple dynamics to complex real-world applications. These comprehensive notes serve as a valuable resource for academic and competitive exam preparation.

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