Introduction
The Laws of Motion are fundamental principles that describe the relationship between the motion of an object and the forces acting on it. These laws, formulated by Sir Isaac Newton, are crucial for understanding classical mechanics and are a significant part of the NEET Physics syllabus. This study note will break down each of Newton's three laws of motion, explain their implications, provide examples, and address common misconceptions.
Newton's First Law of Motion
Statement
Newton's First Law of Motion states: "An object at rest will remain at rest, and an object in motion will continue in motion with a constant velocity unless acted upon by a net external force."
Explanation
This law is also known as the Law of Inertia. It implies that in the absence of a net external force, the state of motion of an object will not change. Inertia is the property of an object to resist changes in its state of motion.
Mathematical Formulation
If the net external force $F_{\text{net}}$ acting on an object is zero, then the acceleration $a$ of the object is zero: $$ F_{\text{net}} = 0 \implies a = 0 $$
Examples
Example- A book on a table: A book resting on a table will remain at rest unless someone applies a force to move it.
- A hockey puck on ice: A hockey puck sliding on ice will continue to slide with a constant velocity if no frictional force acts on it.
Inertia depends on mass; heavier objects have more inertia.
Newton's Second Law of Motion
Statement
Newton's Second Law of Motion states: "The acceleration of an object is directly proportional to the net external force acting on it and inversely proportional to its mass."
Mathematical Formulation
The second law can be expressed as: $$ F_{\text{net}} = ma $$ where:
- $F_{\text{net}}$ is the net external force,
- $m$ is the mass of the object,
- $a$ is the acceleration.
Explanation
This law quantifies the effect of forces on an object's motion. It tells us that a larger force results in a larger acceleration, and a larger mass results in a smaller acceleration for the same force.
Units
- Force ($F$) is measured in Newtons (N).
- Mass ($m$) is measured in kilograms (kg).
- Acceleration ($a$) is measured in meters per second squared ($\text{m/s}^2$).
Examples
Example- Pushing a car: If you push a car with a force of 300 N and the car has a mass of 1500 kg, the acceleration $a$ can be calculated as: $$ a = \frac{F_{\text{net}}}{m} = \frac{300 , \text{N}}{1500 , \text{kg}} = 0.2 , \text{m/s}^2 $$
- Falling objects: A 1 kg object falling under gravity (assuming $g = 9.8 , \text{m/s}^2$) experiences a force: $$ F_{\text{net}} = mg = 1 , \text{kg} \times 9.8 , \text{m/s}^2 = 9.8 , \text{N} $$
A common mistake is to confuse weight with mass. Weight is the force due to gravity and is given by $W = mg$, while mass is the amount of matter in an object.
Newton's Third Law of Motion
Statement
Newton's Third Law of Motion states: "For every action, there is an equal and opposite reaction."
Explanation
This law means that forces always come in pairs. If object A exerts a force on object B, then object B exerts an equal and opposite force on object A.
Examples
Example- Rocket propulsion: A rocket expels gas downwards (action), and the rocket is pushed upwards (reaction).
- Walking: When you walk, your foot pushes backward on the ground (action), and the ground pushes your foot forward (reaction).
Remember that action and reaction forces act on different objects and are equal in magnitude but opposite in direction.
Free-Body Diagrams
Free-body diagrams are essential tools for visualizing the forces acting on an object. They help in applying Newton's Laws of Motion to solve problems.
Steps to Draw a Free-Body Diagram
- Identify the object of interest.
- Draw the object as a point or a simple shape.
- Draw vectors representing all the forces acting on the object. Label each force.
- Indicate the direction of each force.
Forces to consider include gravitational force, normal force, frictional force, tension, and applied forces.
![A free-body diagram of a block on an inclined plane showing gravitational force, normal force, and frictional force.]
Applications of Newton's Laws
Inclined Plane
Analyzing motion on an inclined plane involves breaking forces into components parallel and perpendicular to the plane.
Circular Motion
For an object moving in a circle, the centripetal force is required to keep it in circular motion: $$ F_{\text{centripetal}} = \frac{mv^2}{r} $$ where $m$ is the mass, $v$ is the velocity, and $r$ is the radius of the circle.
Friction
Frictional force opposes the relative motion of surfaces in contact. It is given by: $$ F_{\text{friction}} = \mu N $$ where $\mu$ is the coefficient of friction and $N$ is the normal force.
ExampleFor a block of mass 10 kg on a horizontal surface with a coefficient of friction $\mu = 0.5$, the frictional force is: $$ F_{\text{friction}} = \mu mg = 0.5 \times 10 , \text{kg} \times 9.8 , \text{m/s}^2 = 49 , \text{N} $$
Summary
- First Law: An object remains in its state of motion unless acted upon by a net external force.
- Second Law: The net force on an object is equal to the mass of the object multiplied by its acceleration ($F = ma$).
- Third Law: Every action has an equal and opposite reaction.
Understanding and applying these laws are crucial for solving a wide range of problems in mechanics. Use free-body diagrams to visualize forces and ensure to consider all forces acting on an object.
