Laws of Motion is one of the important topics in JEE Main Physics with 3.33% weightage. Candidates can expect at least 1 question to be asked in JEE Main 2022. Every Year around 1-3 questions are asked from the topics Laws of Motion. Therefore we have prepared JEE Main study notes for laws of motion so that candidates can prepare ahead of JEE Main 2022, the official notification for which is expected to be released in the 3^rd week of December 2021. Force, Circular Motion, Newton’s laws, etc are some of the major topics from this section. Check JEE Main Physics Syllabus.

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What are Force and Inertia?

Force

Force can be defined as a push or pull that will change or tends to change the state of rest or uniform motion. The force is a vector quantity.

Inertia

Inertia can be defined as the property of a body due to which a body opposes the changes in itself and its state. We can measure the inertia of a body by measuring the mass of the body. If a body is heavy then greater force will be required to change the state of the body. 

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Newton's Laws of Motion

Newton had proposed three laws motions and they are:

• Newton’s First Law of Motion: Newton’s first law of motion states that if the net external force on a body is zero, then that body will remain at rest or it will move with a constant velocity. This law defines inertia therefore it is also called as the law of inertia. 

• Newton’s Second Law of Motion: Newton’s second law of motion provides us the definition of force. According to Newton’s second law of motion, the acceleration of an object is directly proportional to the total force applied or acting on it and is inversely proportional to the mass. 

• Newton’s Third Law of Motion: Newton’s third law of motion states that to every action there is an equal and opposite reaction. 

Example of Numerical Value Type Question from Newton’s Law of Motion

Question: Let us consider that a mass of 10 kg is suspended vertically with the help of a rope from the roof. On that rope at some a horizontal force is applied then the rope deviated at an angle of 45∘ at the roof point. If the suspended mass is at equilibrium, the magnitude of the force (in newton) applied is (g=10ms−2)

Answer: 100

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What are Momentum and Impulse?

Momentum

Momentum is represented by p

p=mv; where m is equal to the mass of the body or object and v is equal to the velocity of the body. Therefore momentum can be defined as the product of mass and velocity.

Impulse

When a large amount of force is applied or acts for an extremely short period of time then the total effect of the force is called Impulse.

Conservation Law of Momentum

According to the Conservation Law of Momentum, the net or total change in the linear momentum will be zero in the absence of external force.

Applications of Conservation Law of Momentum

• The Recoil of a Gun: The Conservation Law of Momentum can be defined very easily by the gun and bullet working system. Both gun and bullet are at rest before firing and at that time momentum of the system is zero. But when the bullet is fired, the movement of the bullet is forward and the movement of the recoil is backward. Here due to the difference in mass of bullet and gun that is the mass of gun is very large in comparison to bullet therefore the recoils is small as compared to the velocity of a bullet.

Example of Sample Question on Recoil of Gun

For Example: Before Firing-

Total Mass= m1 + m2

Velocity v=0, because the system was at rest

Therefore, Momentum = mass X velocity = 0

For Example: After Firing- 

Total Mass= m1 +m2

Velocity v= 150m/s

Therefore, Momentum = 3 + 2v’

• The Motion of Rocket: Rockets also work on the Conservation Law of Momentum. The gases in the rocket burn out with a large momentum and due to this the rocket gains an equal and opposite momentum which enables the rocket and engine with a very high velocity. 

• The Man and the Boat: A man is standing on the boat. At that time the momentum of both man and boat is zero. When the man jumps from the boat towards the shore, the man gains the momentum in the forward direction. According to the Conservation Law of Momentum the boat gains the equal momentum in the backward or opposite direction and the boat slightly moves. 

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Equilibrium of a Particle

An object or body or particle will be in equilibrium until when the net or total external force acting on it will remain zero. At this point, the object or body or particle will be either in rest or in uniform motion. 

For Example

As shown in figure below the object A will remain in equilibrium when the total external force on that object is zero. 

F(net) = F1 + F2 + F3 + F4 + F5 = 0

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What is Friction and its types?

Friction

Friction can be defined as a contact force that opposes the relative motion of two bodies. Friction is also self-adjusting in nature.

For Example

Let us consider that the force F is applied on the object and the object is placed on the plane surface. Then the Friction Force is where N is the Normal force and μ is the coefficient of friction force. 

Types of Friction

• Static Friction: Static Friction is the type of friction force that acts on a body or object when there is no other relative motion between that object and the surface. 

Static Friction force is where “μs” is the coefficient of static friction and N is the Normal force. 

• Kinetic Friction: Kinetic friction which is also known as sliding friction is the type of friction that opposes the relative motion between the surfaces that are in contact. 

Kinetic Friction force is where “μk” is the coefficient of kinetic friction and N is the Normal force. 

• Rolling Friction: The other name of rolling friction is also sliding friction that can be defined as friction that will resist the motion of the body when a body is rolling on the surface. 

Rolling Friction force is where “μr” is the coefficient of rolling friction and N is the Normal force. 

Example of Statement Questions on Friction

Question: Select the correct statement which is true in case of Friction

• Rolling friction is greater than sliding friction
• Rolling friction is less than sliding friction 
• Rolling friction is equal to sliding friction
• Rolling friction and sliding friction are the same

Answer: Rolling friction is less than sliding friction

Example of How to Calculate Angle of Friction?

The angle of friction can be defined as an angle between “N” that is a normal reaction and the resultant force of friction that is “f”.

So the Angle of Friction can be represented as:

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What is Circular Motion?

When an object or body moves in a circular path then that motion of the object is known as circular motion. During the time when a body or object is moving in the circular path then at that time, it experiences a force that acts towards the radius of the circular path. This force is known as the Centripetal Forces which is required to move an object or body on a circular path.

Centripetal Force is where v is the velocity of the object or the body and r is the radius of the circular path in which the object is moving. 

Types of Circular Motion

Non Uniform Circular Motion: As the name defines itself in Non Uniform Circular motion an object is moving in the circular path but the speed of that object is not constant then at that time the motion of that object is known as Non Uniform Circular Motion. 

When the body is moving in Non Uniform Circular Motion then the net acceleration of the moving body has two components.

• Radical Acceleration: Radical Acceleration is because of the changes in the direction of the velocity. 

• Tangential Acceleration: Tangential Acceleration is because of the changes in the magnitude of the velocity. 

Net Acceleration of the object can be defined as

Uniform Circular Motion: Uniform circular motion occurs when an object follows the circular path with a constant speed and that motion of the object or the body is called uniform circular motion.

Application of Uniform Circular Motion

• Banking of Roads: Whenever we move or travel in the circular path then we all have noticed that the roads are banked at some angle. This is done so that the vehicle can get the required centripetal force. 

The maximum velocity that is required by the car to take a circular turn without slipping is where “μs” is the coefficient of friction force that is required between the tires of the car and the road, R is the radius of the circular path. 

Also in another case, if a vehicle moves on that curved path with velocity “v” and the radius of curved path “r” then the track is banked by an angle that can be represented as

• Satellite Orbiting around the Earth: A satellite orbits around the earth in a circular orbit and here again to move around the circular path centripetal force is required and this force is provided by the gravitational force between them. 

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Tips to Solve the Questions on Laws of Motion 

1. Question: Let us consider that a body of mass 10kg is having an acceleration of 5m/s2. What will be the net force experienced by it?

Tip to Solve the Question: In the questions where mass and acceleration are given you can use Newton’s Second Law of Motion

Solution: 50N

2. Question: A car with a mass of 1100 kg can accelerate on a level road from rest to 2m/s in 14s. What is the steepest slope this car can climb?

Tip to Solve the Question: While solving this question you have to keep in mind that the plane is smooth. 

Solution: The steepest slope this car can climb is 0.83 degree.

3. Question: A truck is hauling a trailer along a level road. The mass of the truck is m1=8500kg and that of the trailer is m2=27000kg.The 2 moves with an acceleration of a=0.78m/s^2. Ignore the forces of friction and air resistance.

(a)The magnitude of the tension in the horizontal drawbar between the trailer and the truck?

(b)The force that propels the truck forward?

Tip to Solve the Question: Candidates can solve this question by using Newton’s third law of Motion. If you draw a rough figure or if a figure is given in the question then you clearly see that third law of motion is applicable. 

Solution: (a) 21060 N, (b) 27690 N

4. Question: A body has a mass 100 gram, which is tied at the end of a string of length 3 m and rotates in a vertical circle. This body is just able to complete the circle. Now let us consider that if the tension in the string is at its lowest point that is 3.7 N, then what will e its angular velocity will be. Also consider g = 10 m/s2

Tip to Solve the Question: From the question, we can understand that the object is moving in the circle and we have to calculate the velocity so here you have to use the application of Circular motion to get the answer.

Solution: 3 rad/s

5. Question: A block of marble with a mass of 2 kg lying on ice when given a velocity of 6m/s is stopped by friction in 10 sec. Then the what will be the coefficient of friction?

Tip to Solve the Question: This is a direct question and can be directly solved by using the formula for friction.

Solution: 0.06

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Important Formulas in Laws of Motion 

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Tricks to Remember while solving Laws of Motion Questions

• Always start your solution by creating a rough sketch or diagram for the question. This helps you in getting a better understanding of that problem. 
• Mention all the information that is given in the question in your rough or freehand diagram. Like mention force, mass, acceleration, etc. 
• Newton’s third law of motion can be used wherever it is necessary. 
• Identify the principles involved in the problem.
• You have to determine before solving that the question includes Newton’s laws of motion or not, if not then you can approach the question from a different point of view. 
• If something or some value is unknown then it should be left as it is and determined with the help of the laws of motion